Q: Which of the following correctly expresses the double angle formula for sine?

$$\Sen 2a = 2 \Sen a \times \Cos a$$

Q: A medical device rotates at an angle $$a$$ and then at angle $$b. $$What is the cosine of the sum of these angles?

$$\Cos(a+b) = \Cos a \times \Cos b - \Sen a \times \Sen b$$

Q: A satellite moves from angle $$a to $$angle $$b. $$What is the formula for $$\Cos(a-b)$$?

$$\Cos(a-b) = \Cos a \times \Cos b + \Sen a \times \Sen b$$

Q: Which formula gives the tangent of the sum of two angles?

$$\Tg(a+b) = \frac{\Tg a + \Tg b}{1 + \Tg a \times \Tg b}$$

Q: A wheel rotates through angles $$a$$ and $$b. $$What is the formula for $$\Sen(a+b)$$?

$$\Sen(a+b) = \Sen a \times \Cos b + \Cos a \times \Sen b$$

Question 1

Which of the following correctly expresses the double angle formula for sine?

Accepted Answer

$$\Sen 2a = 2 \Sen a 	imes \Cos a$$

Question 2

A medical device rotates at an angle $$a$$ and then at angle $$b. $$What is the cosine of the sum of these angles?

Accepted Answer

$$\Cos(a+b) = \Cos a 	imes \Cos b - \Sen a 	imes \Sen b$$

Question 3

Which formula represents the fundamental trigonometric identity?

Accepted Answer

$$\$$Sen^2$$ x + \$$Cos^2$$ x = 1$$

Question 4

A ramp is built at an angle $$x to $$the ground. If $$\Sen x = 0.6$$ and $$\Cos x = 0.8$$, what is $$\Tg x$$?

Accepted Answer

$$\Tg x = 0.75$$

Question 5

Which expression correctly defines the secant function?

Accepted Answer

$$\Sec x = \frac{1}{\Cos x}$$

Question 6

A satellite moves from angle $$a to $$angle $$b. $$What is the formula for $$\Cos(a-b)$$?

Accepted Answer

$$\Cos(a-b) = \Cos a 	imes \Cos b + \Sen a 	imes \Sen b$$

Question 7

If $$\Sen x = 0.5$$ and $$\Cos x = 0.866$$, what is $$\$$Sen^2$$ x + \$$Cos^2$$ x$$?

Accepted Answer

$$1$$

Question 8

Which formula gives the tangent of the sum of two angles?

Accepted Answer

$$\Tg(a+b) = \frac{\Tg a + \Tg b}{1 + \Tg a 	imes \Tg b}$$

Question 9

A ladder leans against a wall forming angle $$x$$ with the ground. If $$\Cos x = 0.6$$, what is $$\Sec x$$?

Accepted Answer

$$\Sec x = 1.67$$

Question 10

Which formula represents the double angle for cosine?

Accepted Answer

$$\Cos 2a = \$$Cos^2$$ a - \$$Sen^2$$ a$$

Question 11

If $$\Tg x = 2$$, what is $$\Cot x$$?

Accepted Answer

$$\Cot x = 0.5$$

Question 12

A chemical reaction requires the angle $$x$$ such that $$\Sen x = 0.8$$ and $$\Cos x = 0.6. $$What is $$\Tg x$$?

Accepted Answer

$$\Tg x = 1.33$$

Question 13

Which formula correctly defines the cosecant function?

Accepted Answer

$$\Cossec x = \frac{1}{\Sen x}$$

Question 14

If $$\Sen x = 0.6$$ and $$\Cos x = 0.8$$, what is $$\$$Cos^2$$ x - \$$Sen^2$$ x$$?

Accepted Answer

$$0.28$$

Question 15

A wheel rotates through angles $$a$$ and $$b. $$What is the formula for $$\Sen(a+b)$$?

Accepted Answer

$$\Sen(a+b) = \Sen a 	imes \Cos b + \Cos a 	imes \Sen b$$

Question 16

Which formula defines the cotangent function?

Accepted Answer

$$\Cot x = \frac{\Cos x}{\Sen x}$$

Question 17

If $$\Sen x = 0.5$$ and $$\Cos x = 0.866$$, what is $$\Cos 2x$$?

Accepted Answer

$$0.5$$

Question 18

A bridge is designed with an angle $$x$$ such that $$\Cos x = 0.7. $$What is $$\Sec x$$?

Accepted Answer

$$1.43$$

Question 19

Which formula gives the tangent squared in terms of secant squared?

Accepted Answer

$$\Tg^2$ x + 1 = \$$Sec^2$$ x$$

Question 20

If $$\Sen x = 0.6$$ and $$\Cos x = 0.8$$, what is $$\Sen 2x$$?

Accepted Answer

$$0.96$$

Trigonometric Functions and Identities: Study Notes

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