Exercise 38 Page 963

We want to use a Half-Angle Identity to find the exact value of sin 90^(∘). Let's recall the Half-Angle Identity that involves cosine. sin A/2 = ± sqrt(1-cos A/2) Now, we can use this formula to find the value of sin 90^(∘). We will start by rewriting 90^(∘) as a quotient.

Next, we will recall the value of sine, cosine, and tangent for some special angles.

We can see in the table that cos 30^(∘) = sqrt(3)2. Therefore, we can substitute this value into our expression.

Finally, we will determine the sign. To do so, let's recall the signs of sine, cosine, and tangent in the four quadrants of the coordinate plane.

Since 90^(∘) is located between quadrants I and II, we know that sin 90^(∘) is positive. sin 90 ^(∘)= 1