Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3E>Q 11

EASY

AS and A Level

IMPORTANT

Earn 100

Express $\sqrt{5} \cos θ + 2 \sin θ$ in the form $R \cos (θ - α),$ where $R > 0$ and $0 ° < α < 90 °$ Give the value of $α$ correct to $2$ decimal places.Find the smallest positive angle $θ$ that satisfies the equation $\sqrt{5} \cos \frac{1}{2} θ + 2 \sin \frac{1}{2} θ = - 1 .$

Important Questions on Trigonometry

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3E>Q 12

Given that

3 \sec θ + 4 cosec θ = 2 cosec 2 θ,

show that

3 \sin θ + 4 \cos θ = 1 .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3E>Q 12

Express

3 \sin θ + 4 \cos θ

in the form

R \sin (θ + α),

where

R > 0

and

0 ° < α < 90 °

Give the value of

α

correct to

2

decimal places.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3E>Q 12

Express

3 \sin θ + 4 \cos θ

in the form

R \sin (θ + α),

where

R > 0

and

0 ° < α < 90 °

Give the value of

α

correct to

2

decimal places.Hence solve the equation

3 \sec θ + 4 cosec θ = 2 cosec 2 θ

for

0 ° < θ < 360 ° .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3E>Q 13

Express

\sin (θ + 30 °) + \cos θ

in the form

R \sin (θ + α),

where

R > 0

and

0 ° < α < 90 ° .

Give the exact values of

R

and

α .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3E>Q 13

Express

\sin (θ + 30 °) + \cos θ

in the form

R \sin (θ + α),

where

R > 0

and

0 ° < α < 90 ° .

Give the exact values of

R

and

α .

Hence solve the equation

\sin (θ + 30^{\circ}) + \cos θ = 1

for

0^{\circ} < θ < 360^{\circ}

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3E>Q 14

If the maximum and minimum values of

7 \sin^{2} θ + 9 \cos^{2} θ + 4 \sin θ \cos θ + 2

are

a

and

b

, find

a + b

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>EXERCISE 3E>Q 14

Find the maximum and minimum values of

7 \sin^{2} θ + 9 \cos^{2} θ + 4 \sin θ \cos θ + 2

. Hence, or otherwise, solve the equation

7 \sin^{2} θ + 9 \cos^{2} θ + 4 \sin θ \cos θ = 10

for

0^{°} < θ < 360^{°}

. If the values of

θ

are

a, b, c, d

then find

a + b + c + d

in degrees.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 3 - Trigonometry>END-OF-CHAPTER REVIEW EXERCISE 3>Q 1

Write down the amplitude of

y = 3 \sec (2 x - 90 °)

for

0 ° < x < 180 ° .