Question

If sin tetha=root3/2, what is cos tetha?​

Answer 1

Answer:

The value of cos Ф is ± $\frac{1}{2}$

Step-by-step explanation:

There are important rules for sin Ф and cos Ф

• sin²Ф + cos²Ф = 1

• sin²Ф = 1 - cos²Ф

• cos²Ф = 1 - sin²Ф

∵ sin Ф = $\frac{\sqrt{3}}{2}$

∴ sin²Ф = $(\frac{\sqrt{3}}{2})^{2}$

∴ sin²Ф = $\frac{3}{4}$

→ By using the third rule above

∵ cos²Ф = 1 - sin²Ф

∴ cos²Ф = 1 - $\frac{3}{4}$

∴ cos²Ф = $\frac{1}{4}$

→ Take square root for both sides

∴ cos Ф = ± $\frac{1}{2}$

∴ The value of cos Ф is ± $\frac{1}{2}$