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Example Question #1 : Find The Value Of Any Of The Six Trigonometric Functions
Solve the following:
Rewrite in terms of sine and cosine functions.
Since these angles are special angles from the unit circle, the values of each term can be determined from the x and y coordinate points at the specified angle.
Solve each term and simplify the expression.
Example Question #2 : Find The Value Of Any Of The Six Trigonometric Functions
Find the value of .
Using trigonometric relationships, one can set up the equation
.
Solving for ,
Thus, the answer is found to be 29.
Example Question #3 : Find The Value Of Any Of The Six Trigonometric Functions
Find the value of .
Using trigonometric relationships, one can set up the equation
.
Plugging in the values given in the picture we get the equation,
.
Solving for ,
.
Thus, the answer is found to be 106.
Example Question #1 : Find The Value Of Any Of The Six Trigonometric Functions
Find all of the angles that satistfy the following equation:
OR
OR
The values of that fit this equation would be:
and
because these angles are in QI and QII where sin is positive and where
.
This is why the answer
is incorrect, because it includes inputs that provide negative values such as:
Thus the answer would be each multiple of
and
, which would provide the following equations:
OR
Example Question #5 : Find The Value Of Any Of The Six Trigonometric Functions
Evaluate:
To evaluate , break up each term into 3 parts and evaluate each term individually.
Simplify by combining the three terms.
Example Question #1 : Find The Value Of Any Of The Six Trigonometric Functions
What is the value of ?
Convert in terms of sine and cosine.
Since theta is radians, the value of
is the y-value of the point on the unit circle at
radians, and the value of
corresponds to the x-value at that angle.
The point on the unit circle at radians is
.
Therefore, and
. Substitute these values and solve.
Example Question #7 : Find The Value Of Any Of The Six Trigonometric Functions
Solve:
First, solve the value of .
On the unit circle, the coordinate at radians is
. The sine value is the y-value, which is
. Substitute this value back into the original problem.
Rationalize the denominator.
Example Question #8 : Find The Value Of Any Of The Six Trigonometric Functions
Find the exact answer for:
To evaluate , solve each term individually.
refers to the x-value of the coordinate at 60 degrees from the origin. The x-value of this special angle is
.
refers to the y-value of the coordinate at 30 degrees. The y-value of this special angle is
.
refers to the x-value of the coordinate at 30 degrees. The x-value is
.
Combine the terms to solve .
Example Question #9 : Find The Value Of Any Of The Six Trigonometric Functions
Find the value of
.
The value of refers to the y-value of the coordinate that is located in the fourth quadrant.
This angle is also
from the origin.
Therefore, we are evaluating .
Example Question #10 : Find The Value Of Any Of The Six Trigonometric Functions
Simplify the following expression:
Simplify the following expression:
Begin by locating the angle on the unit circle. -270 should lie on the same location as 90. We get there by starting at 0 and rotating clockwise
So, we know that
And since we know that sin refers to y-values, we know that
So therefore, our answer must be 1
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