Take this Quiz: A-Level Maths: Trigonometry | Zestly

Question 1

Which of the following trigonometric identities are valid for all values of $	heta$ where the functions are defined?

Accepted Answer

$1 + 	an^2(	heta) = \sec^2(	heta)$

Question 2

For small values of $	heta$ measured in radians, which of the following approximations are standard?

Accepted Answer

$\sin(	heta) \approx 	heta$

Question 3

If $\cos(A) = \frac{3}{5}$ and $\sin(B) = \frac{5}{13}$, where $A$ and $B$ are acute angles, what is the exact value of $\sin(A+B)$?

Accepted Answer

$\frac{56}{65}$

Question 4

Which of the following expressions are equivalent to $\cos(2	heta)$?

Answer

$\cos^2(	heta) - \sin^2(	heta)$

Answer

$2\cos^2(	heta) - 1$

Answer

$1 - 2\sin^2(	heta)$

Answer

$\cos^2(	heta) + \sin^2(	heta)$

Question 5

Express $3\cos(	heta) + 4\sin(	heta)$ in the form $R\cos(	heta - \alpha)$, where $R > 0$ and $0 < \alpha < \frac{\pi}{2}$. What are the values of $R$ and $	an(\alpha)$?

Answer

$R=5, 	an(\alpha) = 3/4$

Answer

$R=7, 	an(\alpha) = 4/3$

Answer

$R=5, 	an(\alpha) = 4/3$

Answer

$R=7, 	an(\alpha) = 3/4$