Question

Match the following trigonometric expression with its correct value.

PICTURE IS ATTACHED BELOW

Answer 1

Hello!

The answers are:

1 - Tan(120°)

`tan(120)=-√(3)`

2 - Sin(120°)

`sin(120)=(√(3) )/(2)`

3 - cos(150)

`cos(150)=-(√(3) )/(2)`

4 - Cos(135°)

`cos(135)=-(√(2) )/(2)`

5 - Sin(135)

`sin(135)=(√(2) )/(2)`

Why?

To solve this problem, we need to remember the following identity:

`tan\alpha =(sin\alpha )/(cos\alpha)`

Also, we need to program our calculator to the degree mode.

So, solving we have:

1 - Tan(120°)

`tan(120)=(sin(120))/(cos(120))=((√(3) )/(2) )/(-(1)/(2))\\\\((√(3) )/(2) )/(-(1)/(2))=(√(3) )/(2) *{-(2)/(1)}=-√(3)`

2 - Sin(120°)

`sin(120)=(√(3) )/(2)`

3 - cos(150)

`cos(150)=-(√(3) )/(2)`

4 - Cos(135°)

`cos(135)=-(√(2) )/(2)`

5 - Sin(135°)

`sin(135)=(√(2) )/(2)`

Have a nice day!

Answer 2

Answer:

1. tan 120° = -√3

2. sin 120° = √3/2

3. cos 150° = -√3/2

4. cos 135° = -√2/2

5. sin 135° = √2/2

Explanation:

* Lets study the unit circle and the four quadrant

- Any point on the unit circle has x- coordinate = cos(x) and

y-coordinate = sin(x), where x is the angle between the positive

part of the x-axis and the radius of the unit circle

- In the first quadrant all the trigonometry functions are +ve

- In the second quadrant sin(x) only is +ve

- In the third quadrant tan(x) only is +ve

- In the fourth quadrant cos(x) only is +ve

- Look to the attached figure

* Now lets solve the problem

1. tan 120°

- Angle 120° is equivalent to angle 60° in the 1st quadrant

∵ 120° in the 2nd quadrant

∴ tan 120° is negative

∵ tan 60° = √3

∴ tan 120° = -√3

2. sin 120°

- Angle 120° is equivalent to angle 60° in the 1st quadrant

∵ 120° in the 2nd quadrant

∴ sin 120° is positive

∵ sin 60° = √3/2

∴ sin 120° = √3/2

3. cos 150°

- Angle 150° is equivalent to angle 30° in the 1st quadrant

∵ 150° in the 2nd quadrant

∴ cos 150° is negative

∵ cos 30° = √3/2

∴ cos 150° = -√3/2

4. cos 135°

- Angle 135° is equivalent to angle 45° in the 1st quadrant

∵ 135° in the 2nd quadrant

∴ cos 135° is negative

∵ cos 45° = √2/2

∴ cos 135° = -√2/2

5. sin 135°

- Angle 135° is equivalent to angle 45° in the 1st quadrant

∵ 135° in the 2nd quadrant

∴ sin 135° is positive

∵ sin 45° = √2/2

∴ sin 135° = √2/2