FM 11 4.1 Exploring the Primary Trigonometric Ratios of Obtuse Angles
Until now, you have used the primary trigonometric ratios only with acute angles. Here we will
investigate the values of the primary trigonometric ratios for obtuse angles.
θ
sinθ
cosθ
tanθ
(180°-θ)
sin(180°-θ)
cos(180°-θ)
tan(180°-θ)
90°
100°
110°
120°
130°
140°
150°
160°
170°
180°
What relationships do you observe when comparing the trigonometric ratios for obtuse angles
with the trigonometric ratios for the related supplementary acute angle?
Sinθ and Sin(180-θ)
Cosθ and Cos(180-θ)
Tanθ and Tann(180-θ)
Try these:
1. Determine if each of the following equations is true. Explain your answer:
a) tan 48  tan132
b) cos30   cos 60
c) cos 20   cos160
d) sin100   sin80
2. Calculate sin 62 to four decimal places. Predict another angle that has the same ratio
as sin 62 .
3. Calculate tan 96 to four decimal places. Predict another angle that has the same ratio
as tan 96 .
4. Find the acute angle A if sin A  .47 .
5. Find the supplementary angle to A in question 4.
6. Explain what you notice about the sine of the angle you found in question 5 to the sine
of angle A in question 4.