Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
5. The Sine and Cosine Ratios
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Exercise 16 Page 498

The cosine of an acute angle is equal to the sine of its complement.

sin 72^(∘)

Practice makes perfect
We want to write cos 18^(∘) in terms of sine. To do so, let's recall an important property of the sine and cosine of complementary angles.

The cosine of an acute angle is equal to the sine of its complement.

Keep in mind that complementary angles add up to 90^(∘). To find the complement of 18, we subtract our given angle from 90. Now, we can rewrite cos 18^(∘) in terms of sine. cos 18^(∘) = sin(90^(∘)-18^(∘)) = sin 72^(∘)