The answers are:
1 - Tan(120°)
[tex]tan(120)=-\sqrt{3}[/tex]
2 - Sin(120°)
[tex]sin(120)=\frac{\sqrt{3} }{2}[/tex]
3 - cos(150)
[tex]cos(150)=-\frac{\sqrt{3} }{2}[/tex]
4 - Cos(135°)
[tex]cos(135)=-\frac{\sqrt{2} }{2}[/tex]
5 - Sin(135)
[tex]sin(135)=\frac{\sqrt{2} }{2}[/tex]
To solve this problem, we need to remember the following identity:
[tex]tan\alpha =\frac{sin\alpha }{cos\alpha}[/tex]
Also, we need to program our calculator to the degree mode.
So, solving we have:
1 - Tan(120°)
[tex]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}[/tex]
2 - Sin(120°)
[tex]sin(120)=\frac{\sqrt{3} }{2}[/tex]
3 - cos(150)
[tex]cos(150)=-\frac{\sqrt{3} }{2}[/tex]
4 - Cos(135°)
[tex]cos(135)=-\frac{\sqrt{2} }{2}[/tex]
5 - Sin(135°)
[tex]sin(135)=\frac{\sqrt{2} }{2}[/tex]
Have a nice day!
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
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
