All Precalculus Resources
Solve the following:
Correct answer:
Explanation:
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.
Find the value of .
Correct answer:
Explanation:
Using trigonometric relationships, one can set up the equation
.
Solving for ,
Thus, the answer is found to be 29.
Find the value of .
Correct answer:
Explanation:
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.
Find all of the angles that satistfy the following equation:
Correct answer:
OR
Explanation:
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
Evaluate:
Correct answer:
Explanation:
To evaluate , break up each term into 3 parts and evaluate each term individually.
Simplify by combining the three terms.
What is the value of ?
Correct answer:
Explanation:
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.
Solve:
Correct answer:
Explanation:
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.
Find the exact answer for:
Correct answer:
Explanation:
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 .
Find the value of
.
Correct answer:
Explanation:
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 .
Simplify the following expression:
Correct answer:
Explanation:
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