All ACT Math Resources
Example Question #67 : Trigonometry
If , what is ? Round to the nearest hundredth.
Recall that the sine wave is symmetrical with respect to the origin. Therefore, for any value , the value for is . Therefore, if is , then for , it will be .
Example Question #1 : How To Find Positive Sine
In a right triangle, cos(A) = . What is sin(A)?
In a right triangle, for sides a and b, with c being the hypotenuse, . Thus if cos(A) is , then c = 14, and the side adjacent to A is 11. Therefore, the side opposite of angle A is the square root of , which is Since sin is , sin(A) is .
Example Question #2 : How To Find Positive Sine
What is the value of ?
As with all trigonometry problems, begin by considering how you could rearrange the question. They often have hidden easy ways out. So begin by noticing:
Now, you can treat like it is any standard denominator. Therefore:
Combine your fractions and get:
Now, from our trig identities, we know that , so we can say:
Now, for our triangle, the is . Therefore,
Example Question #3 : How To Find Positive Sine
Solve for :
Recall that the standard triangle, in radians, looks like:
Since , you can tell that .
Therefore, you can say that must equal :
Solving for , you get: