ACT Math : How to find positive sine

Example Questions

Example Question #1 : How To Find Positive Sine

If , what is ?  Round to the nearest hundredth.

Explanation:

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 #2 : How To Find Positive Sine

In a right triangle, cos(A) = . What is sin(A)?

Explanation:

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 #3 : How To Find Positive Sine

What is the value of ?

Explanation:

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:

Now, from our trig identities, we know that , so we can say:

Now, for our triangle, the  is . Therefore,

Example Question #21 : Sine

Solve for :

if

Explanation:

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: