How To Solve For Theta

The police of Tangent which is also called as tangent formula or tangent dominion is the ratio of the sine of the angle to the cos of the angle.

Tan Θ = Contrary / Adjacent

Tan x formula

The Tan Θ is the ratio of the Opposite side to the Next, where (Θ) is one of the astute angles.

\(\begin{array}{fifty}Tan \Theta = \frac{Opposite Side}{Adjacent Side}\end{array} \)

Tan Theta Formula

Out of other 6 trigonometric formulas, let'due south take a look at the practice question of tan theta formula.

Example i:

If Sin ten = 4/v, Find the value of Cos x and tan 10?

Solution: Using Trigonometric identities: Cos²x = i- Sin²x

Cos²x = 1 – (4/5)²

= one – 16/25

= (25 – 16) / 25

= nine/25

Cos x =

\(\begin{array}{50}\sqrt{ix/25}\end{array} \)

= ⅗

Tan x = Sin x / Cos x

= (4/v) / (iii/5)

= 4/three

Question one: If Sec 10 = iv/seven, discover the Cos x and tan x?

Solution: As Sec ten = 1/cos ten

4/vii = ane/ cos x

Cos 10 = 7/4

Tan² x = sec²x – ane

= (4/vii)² – 1

= 16/49 – 1

= -33 / 49

Tan x =

\(\begin{array}{l}\sqrt{-33}\stop{array} \)

To practice more Trigonometric questions and understand the trigonometric concepts meliorate, Register on BYJU'Southward.

Source: https://byjus.com/tan-theta-formula/