a Calculate the two side lengths of the right triangle using the sine and cosine ratio.
B
b Did you have to calculate the trigonometric expressions from Part A?
C
c cos^2 θ+sin^2 θ=1
A
a R(0.342,0.940)
B
b R(cos 70^(∘),sin 70^(∘))
C
c See solution.
Practice makes perfect
a Examining the diagram, we see a right triangle inside the unit circle. This right triangle has a hypotenuse of 1. Let's also label the length of the two legs as a and b.
To calculate the coordinates of R, we should find the length of the horizontal and vertical leg of the triangle. With the given information, we can calculate these side lengths by using the cosine and sine rule.
cos 70^(∘) = b/1 & ⇔ b ≈ 0.342 [1em]
sin 70^(∘) = a/1 & ⇔ a ≈ 0.940
Let's add the side length to the diagram.
b In Part A, we calculated the decimal form of sin 70^(∘) and cos 70^(∘). However, we could also just leave the calculations as trigonometric ratios if we want exact values.
c The Pythagorean Identity has the following format.
cos^2 θ+sin^2 θ=1
From Part A, we know that cos 70^(∘) = 0.342 and sin 70^(∘) = 0.940. By substituting these values into the Pythagorean Identity, we can show that it works.
