ACT Math : How to find positive sine

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find Positive Sine

If , what is ?  Round to the nearest hundredth.

Possible Answers:

Correct answer:


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 #71 : Trigonometry

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

Possible Answers:

Correct answer:


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 #72 : Trigonometry


What is the value of ?

Possible Answers:

Correct answer:


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 #73 : Trigonometry

Solve for :


Possible Answers:

Correct answer:


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:


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