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

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

Q: Which of the following is the correct expression for $$\Cos(a+b)$$?

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

Q: A ramp rises $$3$$ meters over a horizontal distance of $$4$$ meters. What is the angle $$\theta$$ the ramp makes with the ground?

$$\theta = \tg$$^{-1}$$(\frac{3}{4})$$

Q: Which of the following is the correct expression for $$\tg(a+b)$$?

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

Q: Which of the following is the correct expression for $$\Cos(a-b)$$?

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

Q: A ship is sailing due east. After $$5 km$$, it changes direction to $$30^\circ$$ north of east and sails another $$10 km. $$What is the total displacement from the starting point?

$$\sqrt{5^2$ + 10^2$ - 2 \times 5 \times 10 \times \Cos 30^\circ}$$

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 ladder leans against a wall making an angle $$	heta$$ with the ground. If the length of the ladder is $$10$$ meters and the angle $$	heta is$$ $$60^\circ$$, what is the height the ladder reaches on the wall?

Accepted Answer

$$10 	imes \Sen 60^\circ$$

Question 3

Which of the following is the correct expression for $$\Cos(a+b)$$?

Accepted Answer

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

Question 4

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

Accepted Answer

$$0.75$$

Question 5

A ramp rises $$3$$ meters over a horizontal distance of $$4$$ meters. What is the angle $$	heta$$ the ramp makes with the ground?

Accepted Answer

$$	heta = 	g$$^{-1}$$(\frac{3}{4})$$

Question 6

Which of the following is the correct fundamental trigonometric identity?

Accepted Answer

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

Question 7

If $$\Cos x = 0.5$$, what is $$\Sec x$$?

Accepted Answer

$$2$$

Question 8

A building casts a shadow of $$15$$ meters when the sun's angle of elevation is $$30^\circ. $$What is the height of the building?

Accepted Answer

$$15 	imes 	g 30^\circ$$

Question 9

Which of the following is the correct expression for $$\Cos 2a$$?

Accepted Answer

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

Question 10

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

Accepted Answer

$$1.33$$

Question 11

Which of the following is the correct expression for $$	g(a+b)$$?

Accepted Answer

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

Question 12

A person is standing $$20$$ meters from a tree. If the angle of elevation to the top of the tree is $$45^\circ$$, what is the height of the tree?

Accepted Answer

$$20 	imes 	g 45^\circ$$

Question 13

Which of the following is the correct definition for $$\Cossec x$$?

Accepted Answer

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

Question 14

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

Accepted Answer

$$1$$

Question 15

Which of the following is the correct definition for $$\Cot x$$?

Accepted Answer

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

Question 16

A pilot flying at an altitude of $$1000$$ meters sees an airport at an angle of depression of $$30^\circ. $$What is the horizontal distance to the airport?

Accepted Answer

$$1000 	imes \Cot 30^\circ$$

Question 17

Which of the following is the correct expression for $$\Sec x$$?

Accepted Answer

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

Question 18

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

Accepted Answer

$$0.5$$

Question 19

Which of the following is the correct expression for $$\Cos(a-b)$$?

Accepted Answer

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

Question 20

A ship is sailing due east. After $$5 km$$, it changes direction to $$30^\circ$$ north of east and sails another $$10 km. $$What is the total displacement from the starting point?

Accepted Answer

$$\sqrt{5^2$ + 10^2$ - 2 	imes 5 	imes 10 	imes \Cos 30^\circ}$$

Trigonometric Identities and Functions: Key Formulas and Relationships

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