Question

Fill in the blank. If necessary, use the slash mark (/) for a fraction bar.

If cos θ = 3/5 , then tanθ = _________. _____________


: sin30 = √3/2 and cos 30 = ½
A: true
B: false

Answer 1

Answer on Question #57922 -Math - Trigonometry

Task:

1. Fill in the blank. If necessary, use the slash mark (/) for a fraction bar.

If $\cos(\theta) = \frac{3}{5}$, then $\tan(\theta) = \_$.

Solution:

1) Use the function inverse cosine (arccosine) to find the angle from the known value of the cosine:

$$\theta = \arccos(\cos(\theta)) = \arccos\left(\frac{3}{5}\right) = 53.13{}^\circ$$

Then,

$$\tan(\theta) = \tan(53.13{}^\circ) = 1.3333$$

2) Also, knowing the value of the angle, the tangent can be found from the relation:

$$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)};$$

Then,

$$\tan(\theta) = \frac{\sin(53.13{}^\circ)}{\cos(53.13{}^\circ)} = 1.3333$$

Answer:

$\tan(\theta) = 1.3333$.

Task:

2. $\sin(30) = \sqrt{\frac{3}{2}}$ and $\cos(30) = \frac{1}{2}$

A: true

B: false

Solution:

$$\sin(30) \neq \sqrt{\frac{3}{2}} \quad \text{and} \quad \cos(30) \neq \frac{1}{2}$$

Because,

$$\cos(30) = \sqrt{\frac{3}{2}} \quad \text{and} \quad \sin(30) = \frac{1}{2}$$

Therefore the original approval is false.

Answer:

B: false.

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