Question

if tan theta = 1 by root 3 what is the value of cos theta​

Answer 1

EXPLANATION.

→ Tan ø = 1/√3

→ To find value of cos ø.

→ Tan ø = P/B = perpendicular/Base.

→ By using the Pythagorean theorem.

→ H² = p² + B²

→ H² = (1)² + (√3)²

→ H² = 1 + 3

→ H² = 4

→ H = 2

→ Sin ø = P/H = 1/2

→ Cos ø = B/H = √3/2

→ Tan ø = P/B = 1/√3

→ Cosec ø = H/P = 2/1

→ Sec ø = H/B = 2/√3

→ Cot ø = B/P = √3/1

Answer 2

Given :

• Tan ø = 1/√3

To Find :

• what is the value of cos theta

Solution :

By Pythagorean theorem :

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

• The sides of this triangle have been named as Perpendicular, Base and Hypotenuse.

• Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

$: \implies \sf \: \: \: \: \: \: \: \: \: \: \: {H}^{2} = {P}^{2} + {B}^{2}$

Substitute all values :

$: \implies \sf \: \: \: \: \: \: \: \: \: \: \: {H}^{2} = {1}^{2} + {( \cancel{ \sqrt{} \: 3} } \: )^{ \cancel{2} } \\ \\ \\ \\ : \implies \sf \: \: \: \: \: \: \: \: \: \: \: {H}^{2} = 1 + 3 \\ \\ \\ : \implies \sf \: \: \: \: \: \: \: \: \: \: \: {H}^{2} = 4 \\ \\ \\ : \implies \sf \: \: \: \: \: \: \: \: \: \: \: H = \sqrt{4} \\ \\ \\ \\ \implies \sf \: \: \: \: \: \: \: \: \: \: \: H = 2$

More to know :

$\bullet\:\sf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}$