Question 1

LEVEL 8

Find the exact value for the following trigonometric value.

2 \text{cos}(30\degree)

Select the correct answer from the list below:

A: \dfrac{1}{2}

B: \dfrac{\sqrt{3}}{3}

C: \sqrt{3}

D: \dfrac{1}{\sqrt{3}}

 

CORRECT ANSWER:  C: \sqrt{3}

WORKED SOLUTION:

\text{cos} (30\degree)=\dfrac{\sqrt{3}}{2}

2 \text{cos} (30\degree)=2\times\dfrac{\sqrt{3}}{2}=\sqrt{3}

Question 2

LEVEL 8

Find the exact value for the following expression.

4 \text{sin} (30\degree) + 3 \text{tan} (45\degree)

Select the correct answer from the list below:

A: 2 + 3\sqrt{3}

B: 7

C: 5

D: 5.5

 

CORRECT ANSWER:   C: 5

WORKED SOLUTION:

\text{sin} (30\degree)=\dfrac{1}{2}

4 \text{sin} (30\degree)=4\times\dfrac{1}{2}=2

\text{tan} (45\degree) = 1

3 \text{tan} (45\degree) = 3 \times 1 = 3

4 \text{sin} (30\degree) + 3 \text{tan} (45\degree) = 2 + 3 = 5

Question 3

LEVEL 8

Find the exact value for the following trigonometric value.

9 \text{tan} (30\degree)

Select the correct answer from the list below:

A:  2\sqrt{3}

B: 3\sqrt{3}

C: \dfrac{3}{\sqrt{3}}

D: \dfrac{2}{\sqrt{3}}

 

CORRECT ANSWER:  B: 3\sqrt{3}

WORKED SOLUTION:

\text{tan} (30\degree)=\dfrac{\sqrt{3}}{3}

9 \text{tan} (30\degree)=9\times\dfrac{\sqrt{3}}{3}=3\sqrt{3}

Question 4

LEVEL 8

Find the exact value for the following expression.

\text{cos}(30\degree) \times \text{sin}(60\degree)

Select the correct answer from the list below:

A: \sqrt{3}

B: \dfrac{3}{4}

C: \dfrac{4}{3}

D: \dfrac{3}{2}

 

CORRECT ANSWER:  B: \dfrac{3}{4}

WORKED SOLUTION:

\text{cos}(30\degree) = \dfrac{\sqrt{3}}{2}

\text{sin}(60\degree) = \dfrac{\sqrt{3}}{2}

\text{cos}(30\degree) \times \text{sin}{60\degree} = \dfrac{\sqrt{3}}{2} \times \dfrac{\sqrt{3}}{2} = (\dfrac{\sqrt{3}}{2})^2 = \dfrac{3}{4}

Question 5

LEVEL 8

Find the exact value for the following trigonometric value.

8 \text{sin}{45\degree}

Select the correct answer from the list below:

A: 4 \sqrt{2}

B: 4\sqrt{3}

C: 2

D: \dfrac{8 \sqrt{3}}{3}

 

CORRECT ANSWER:  A: 4 \sqrt{2}

WORKED SOLUTION:

\text{sin}{45\degree} = \dfrac{1}{\sqrt{2}}

8 \text{sin}{45\degree} = 8 \times \dfrac{1}{\sqrt{2}} = \dfrac{8}{\sqrt{2}} = \dfrac{8\sqrt{2}}{2} = 4 \sqrt{2}