Question

If the sin 30° is one half, then the cos ________° = ________. 60°; one half 30°; square root 2 over 2 60°; square root 3 over 2 30°; 1

Answer 1

Answer:

60°; one half

Step-by-step explanation:

we know that

If two angles are complementary, then sine of one angle equals the cosine of the other angle and vice versa

so

If

$A+B=90^o$

$B=90^o-A$

then

$sin(A)=cos(B)$

substitute the value of B

$sin(A)=cos(90^o-A)$

In this problem we have

$sin(30^o)=\frac{1}{2}$

so

$A=30^o$

substitute the value of A  

$sin(30^o)=cos(90^o-30^o)$

$sin(30^o)=cos(60^o)$

therefore

$cos(60^o)=\frac{1}{2}$