Question

If 2 sin xº - 1 = 0 and xº is an acute angle; find:
(i) sin xº (ii) xº (iii) cos xº and tan xº​

Answer 1

Answer:

sinx=1/2. x=30°. cosx=root3/2. tanx=1/root3

Step-by-step explanation:

2sinx +1=0

2sinx=1

sinx=1/2

x=30°

cosx= cos30°=root3/2

tanx=tan30°=1/root3

Answer 2

Required Answer:-

Given:

• 2sin(x) - 1 = 0

To find:

1. sin(x)
2. x°
3. cos(x)
4. tan(x)

Solution:

Given that,

➡ 2 sin(x) - 1 = 0

➡ 2sin(x) = 1

➡ sin(x) = 1/2 (Answer to question 1)

Now,

➡ sin(x) = 1/2

➡ sin(x) = sin(30) (From T-Ratio Table.)

➡ x = 30° (Answer to question 2)

From trigonometry ratio table,

cos(x)

= cos(30°)

= √3/2 (Answer to question 3)

So,

tan(x)

= sin(x)/cos(x)

= 1/2 ÷ √3/2

= 1/√3 (Answer to question 4)

Trigonometry Ratio table:

$\sf Trigonometric\ Values:- \\\ \boxed{\begin{array}{c|c|c|c|c|c} \sf Angle & 0^{\circ} & 30^{\circ} & 45^{\circ} & 60^{\circ} & 90^{\circ} \\ \sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1 \\ \cos \theta & 1 & \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} & 0 \\ \tan\theta & 0 & \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} & {\infty}\end{array}}$