Sin Tan formula

Sin Tan Formula: The sine function and tangent function depends on the sides of the right-angled triangle. If theta is an angle in a right triangle, then;

Tan Theta = Opposite side to theta / Adjacent side to theta

sin Theta = Opposite side to theta / Hypotenuse of triangle

Sin – Tan x formula

The Tan Theta is the ratio of the Opposite side to the Adjacent, where (Θ) is one of the acute angles.

See the figure of a right triangle below, where theta is an angle and adjacent side (also called base), opposite side (also called perpendicular) and hypotenuse are the three sides.

Tan Sin Formula Questions

Let’s have a look at the practice question of tan theta formula.

Question 1: If Sec x = 7/4, find tan x and sin x?

Solution: As Sec x = 1/cos x

7/4 = 1/ cos x

Cos x = 4/7

Tan²x = sec²x – 1

= (7/4)² – 1

= 49/16 – 1

= 33/16

Tan x = √(33/16)

Sin²x = 1-cos²x
= 1 – (4/7)²
= 1 – 16/49
= 33/49
Sin x = √(33/49)

Question 2: From the following figure find the value of tan A.

Solution:
From the given figure,
sin A = Opposite/Hypotenuse
= BC/AC
= 4/5
By Pythagoras theorem,
AC² = AB² + BC²
5² = AB² + 4²
AB² = 25 – 16
AB² = 9
AB = √9
AB = 3
tan A = Opposite/Adjacent
= BC/AB
= 4/3

Question 3: From the given right triangle ABC, find the values of sin A, tan A, sin C, and tan C.

Solution:
From the given figure,
AB = 12 cm, BC = 5 cm, AC = 13 cm
We know that,
sin x = Side opposite to angle x/Hypotenuse
tan x = Side opposite to angle x/Side adjacent to angle x
Therefore,

sin A = BC/AC = 5/13
tan A = BC/AB = 5/12
sin C = AB/AC = 12/13
tan C = AB/BC = 12/5

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