Mathematics, 26.01.2020 17:31 Angel1107

Match the following trigonometric expression with its correct value.

picture is attached below

Match the following trigonometric expression with its correct value. picture is attached

Answers: 3

Show answers

Answers

Answer from: TrudnEli9904

Hello!

The answers are:

1 - Tan(120°)

$tan(120)=-\sqrt{3}$

2 - Sin(120°)

$sin(120)=\frac{\sqrt{3} }{2}$

3 - cos(150)

$cos(150)=-\frac{\sqrt{3} }{2}$

4 - Cos(135°)

$cos(135)=-\frac{\sqrt{2} }{2}$

5 - Sin(135)

$sin(135)=\frac{\sqrt{2} }{2}$

Why?

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

$tan\alpha =\frac{sin\alpha }{cos\alpha}$

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

So, solving we have:

1 - Tan(120°)

$tan(120)=\frac{sin(120)}{cos(120)}=\frac{\frac{\sqrt{3} }{2} }{-\frac{1}{2}}\\\\\frac{\frac{\sqrt{3} }{2} }{-\frac{1}{2}}=\frac{\sqrt{3} }{2} *{-\frac{2}{1}}=-\sqrt{3}$

2 - Sin(120°)

$sin(120)=\frac{\sqrt{3} }{2}$

3 - cos(150)

$cos(150)=-\frac{\sqrt{3} }{2}$

4 - Cos(135°)

$cos(135)=-\frac{\sqrt{2} }{2}$

5 - Sin(135°)

$sin(135)=\frac{\sqrt{2} }{2}$

Have a nice day!

Answer from: brandonthomas11

1. tan 120° = -√3

2. sin 120° = √3/2

3. cos 150° = -√3/2

4. cos 135° = -√2/2

5. sin 135° = √2/2

Step-by-step 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

Match the following trigonometric expression with its correct value. picture is attached below

Answer from: Quest

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

Answer from: Quest

sine

step-by-step explanation: