Trigonometry : Trigonometry
Study concepts, example questions & explanations for Trigonometry
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Example Questions
Example Question #2 : Angles In The Unit Circle
What is the value of 
To help with this one, draw a 45-45-90 triangle. With legs equal to 1 and a hypotenuse of 
Then, use the definition of tangent as opposite over adjacent to find the value.
Since the legs are congruent, we get that the ratio is 1.
Example Question #3 : Angles In The Unit Circle
What is 
Recall that on the unit circle, sine represents the y coordinate of the unit circle.
Then, since we are at 90˚, we are at the positive y axis, the point (0,1).
At this point on the unit circle, the y value is 1.
Thus 
Example Question #6 : Angles In The Unit Circle
Which of the following is NOT a special angle on the unit circle?
For an angle to be considered a special angle, the angle must be able to produce a 
The only angle that is not capable of the special angles formation is 
Example Question #71 : Unit Circle And Radians
If 
The solution does not lie in the given interval.
We first make the substitution 
In the interval 
Solving for 
Example Question #2 : Angles In The Unit Circle
What is the value of 
From the unit circle, the value of
This can be found using the coordinate pair associated with the angle 
Recall that the 
Example Question #3 : Angles In The Unit Circle
What is
using the unit circle?
Recall that the unit circle can be broken down into four quadrants. Each quadrant has similar coordinate pairs basic on the angle. The only difference between the actual coordinate pairs is the sign on them. In quadrant I all signs are positive. In quadrant II only sine and cosecant are positive. In quadrant III tangent and cotangent are positive and quadrant IV only cosine and secant are positive.
From the unit circle, the coordinate point of
Example Question #8 : Angles In The Unit Circle
Give the exact value.
Use the unit circle to find:
None of the above
Locate 
Sine is related to the why y value of the coordinate point because it is opposite/Hyp.
In other words the 
The coordinate pair for 
Example Question #71 : Unit Circle And Radians
Give the exact value.
Use the unit circle to find:
None of the above
Locate 
Cosine is related to the why x value of the points, because it is Adj/Hyp.
In other words the
The coordinate point of 
Example Question #71 : Unit Circle And Radians
Give the exact value.
Consider the unit circle. What is the value of the given trigonometric function?
Use the unit circle to locate the following:
Recall that the
Since the tangent is equal to the sine divided by the cosine, we need to find the following:
Now, we will use this information to solve the problem.
Substitute the calculated values:
Solve. Remember that dividing by a fraction is the same as multiplying by its reciprocal.
Example Question #1 : Complementary And Supplementary Angles
Determine the value for 
According to the unit circle, an angle of 
Therefore:
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