How to find positive sine - ACT Math
Card 0 of 4
If 
, what is 
? Round to the nearest hundredth.
If
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 
.
Recall that the sine wave is symmetrical with respect to the origin. Therefore, for any value
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In a right triangle, cos(A) = 
. What is sin(A)?
In a right triangle, cos(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 
.
In a right triangle, for sides a and b, with c being the hypotenuse,
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Solve for 
:
if 
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:
Recall that the standard
Since
Therefore, you can say that
Solving for
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What is the value of 
?
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,
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
Combine your fractions and get:
Now, from our trig identities, we know that
Now, for our triangle, the
Compare your answer with the correct one above