Sin, Cos, Tan - Trigonometry

Card 0 of 60

If cos x = 0.2 $\small \cosx$ and sin x = 0.4, what is the value of tan x?

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$\small $\tan{x}$=\frac{\sin{x}$}{$\cos{x}$}$

$\small \small $\tan{x}$=\frac{0.4}{0.2}$$

$\small $\tan{x}$=0.035$

$\small $x=\tan^{-1}$0.035$

$\small x=2$

Find the value of the trigonometric function in fraction form for triangle .

What is the cosine of $\angle B$ ?

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The cosine of an angle is the value of the adjacent side over the hypotenuse.

Therefore:

$cos \angle B = $\frac{adjacent}{hypotenuse}$ = $\frac{7}{25}$$

Which of the following describes the ratio of sine?

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Sine is by definition of sides in a right triangle is opposite side over hypotenuse.

To remember this, use SOH CAH TOA.

SOH: Sine=Opposite/Hypotenuse

CAH: Cosine=Adjacent/Hypotenuse

TOA: Tangent=Opposite/Adjacent

What is the value of ?

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Solve each term separately.

$cos(30)= $\frac{\sqrt3}{2}$$

$cos(60)=\frac{1}{2}$$

Add both terms.

$\frac{\sqrt3}{2}$+\frac{1}{2}$= $\frac{\sqrt3+1}{2}$

Determine the value of .

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Rewrite in terms of sines and cosines.

$2tan(120)=2($\frac{sin(120)}{cos(120)}$)=2($\frac{\frac{\sqrt3}{2}$}{-$\frac{1}{2}$})$

Simplify the complex fraction.

$2($\frac{\frac{\sqrt3}{2}$}{-$\frac{1}{2}$})= 2\times$\frac{\sqrt3}{2}$\times-2 = -2\sqrt3$

Find the value of $$\frac{1}{2}$sin(45)+ tan(60)$ .

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To find the value of $$\frac{1}{2}$sin(45)+ tan(60)$ , solve each term separately.

$\frac{1}{2}$sin(45)=\frac{1}{2}$ \cdot $\frac{\sqrt2}{2}$ = $\frac{\sqrt2}{4}$

$tan(60) = \sqrt3$

Sum the two terms.

$\frac{\sqrt2}{4}$+\sqrt3 = $\frac{\sqrt2}{4}$+\frac{4\sqrt3}{4}$ = $\frac{\sqrt2+4\sqrt3}{4}$

Select the ratio that would give Tan B.

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We need the Tan B. Which side lengths correspond to this ratio?

$\tan=\frac{opp}{adj}$$

Calculate $tan($\frac{4\pi}{3}$)$ .

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The tangent function has a period of $\pi$ units. That is,

$tan(x+n\pi)=tanx$

for all $n\in\mathbb{Z}$ .

Since $$\frac{4\pi}{3}$=\frac{\pi}{3}$+\pi$ , we can rewrite the original expression $tan($\frac{4\pi}{3}$)$ as follows:

$tan($\frac{4\pi}{3}$)=tan($\frac{\pi}{3}$+\pi)$

$=tan($\frac{\pi}{3}$)$

$=\frac{sin(\frac{\pi}{3}$)}{cos($\frac{\pi}{3}$)}$

$=\frac{(\frac{\sqrt{3}$}{2})}{($\frac{1}{2}$)}$

$=$\sqrt{3}$$

Hence,

$tan($\frac{4\pi}{3}$)=$\sqrt{3}$$

Calculate $cos($\frac{5\pi}{3}$)$ .

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First, convert the given angle measure from radians to degrees:

Next, recall that lies in the fourth quadrant of the unit circle, wherein the cosine is positive. Furthermore, the reference angle of is

Hence, all that is required is to recognize from these observations that

,

which is $\frac{1}{2}$ .

Therefore,

$cos($\frac{5\pi}{3}$)=\frac{1}{2}$$

What is the result when the following expression is simplified as much as possible?

$\sin(2h)\sec(h)+2\sin(-h)$

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Because $\sin x$ is an odd function, we can rewrite the second term in the expression.

$2\sin(-h)=-2\sin h$ .

We now use a double-angle formula to expand the first term.

$\sin(2h)\sec h=2\sin h\cos h\sec h$ .

Because they are reciprocals, $\cos h\sec h=1$ .

$2\sin h\cos h\sec h-2\sin h=2\sin h-2\sin h=0.$

Round to the nearest hundredth.

Use your calculator to find:

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Before plugging the function into the calculator make sure the mode of the calculator is set to degrees,

Plug in which equals to .

Round to the nearest hundredth.

Use your calculator to find:

$\cos $\frac{3\pi}{8}$$

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Before plugging the function into the calculator make sure the mode of the calculator is set to radians,

plug in

$\cos $\frac{3\pi}{8}$$

which is equal to .

$\left ( \sin15 + \cos\15 \right $)^{2}$$ What is the closest value to this expression?

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First you have to know the equation for $\left ( a+b\right $)^{2}$ = $a^{2}$$+2ab+b^{2}$$ and apply it to our equation. Second the formula of will allow you to get rid of the square sin and cos. Third the equation $\sin2x = 2\sin \cos$ will allow you to get rid of the . Therefore, we will have a $\sin(30)$ , and that will be equal to . Sum and and you will get

if $\cos x = $\frac{4}{5}$$ What is $\sin2x$ ?

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Remember two things. First if $\cos x=\frac{4}{5}$$ , find the $\sin(x)$ by using the Pythagoras Theorem. If one side is and the hypotenuse is , then the other side is . $\sin x$ will be $\frac{3}{5}$ . Finally remember the formula for $\sin2x = 2\sin x *\cos x$ . And just place the things we found to the equation.

What is the value of cos30o . sin30o . tan60o

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If cos x = 0.2 $\small \cosx$ and sin x = 0.4, what is the value of tan x?

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$\small $\tan{x}$=\frac{\sin{x}$}{$\cos{x}$}$

$\small \small $\tan{x}$=\frac{0.4}{0.2}$$

$\small $\tan{x}$=0.035$

$\small $x=\tan^{-1}$0.035$

$\small x=2$

Find the value of the trigonometric function in fraction form for triangle .

What is the cosine of $\angle B$ ?

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The cosine of an angle is the value of the adjacent side over the hypotenuse.

Therefore:

$cos \angle B = $\frac{adjacent}{hypotenuse}$ = $\frac{7}{25}$$

Which of the following describes the ratio of sine?

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Sine is by definition of sides in a right triangle is opposite side over hypotenuse.

To remember this, use SOH CAH TOA.

SOH: Sine=Opposite/Hypotenuse

CAH: Cosine=Adjacent/Hypotenuse

TOA: Tangent=Opposite/Adjacent

What is the value of ?

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Solve each term separately.

$cos(30)= $\frac{\sqrt3}{2}$$

$cos(60)=\frac{1}{2}$$

Add both terms.

$\frac{\sqrt3}{2}$+\frac{1}{2}$= $\frac{\sqrt3+1}{2}$

Determine the value of .

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Rewrite in terms of sines and cosines.

$2tan(120)=2($\frac{sin(120)}{cos(120)}$)=2($\frac{\frac{\sqrt3}{2}$}{-$\frac{1}{2}$})$

Simplify the complex fraction.

$2($\frac{\frac{\sqrt3}{2}$}{-$\frac{1}{2}$})= 2\times$\frac{\sqrt3}{2}$\times-2 = -2\sqrt3$