Find the Value

Q. Find the value of Sin θ + Cos θ?

The Ratios of Trigonometry

Three major trigonometric ratios, Sine, Cosine, and Tangent, are used to calculate trigonometry values. In trigonometry, the basic values are 0°, 30°, 45°, 60°, and 90°.

• sin θ = Side opposite of θ / Hypotenuse = BC / AC

• cos θ = Adjacent side of θ / Hypotenuse = AB / AC

• tan θ =Side opposite of θ / Adjacent side to θ= BC / AB

We can also write the trigonometric values for reciprocal properties, Sec, Cosec, and Cot ratios in the same way.

• Sec θ = 1/Cos θ = Hypo / Adjacent side to the angle θ = AC / AB

• And Cosec θ = 1/Sin θ = Hypo / Side opposite to angle θ = AC / BC

• Cot θ = 1/tan θ = Adjacent side to the angle θ / Side opposite to the angleθ = AB / BC

The Pythagorean Identities will help in solving this problem.

sin2 θ + cos2 θ = 1, 1 − sin2 θ = cos2 θ 

1 − cos2 θ = sin2 θ, tan2 θ + 1 = sec2 θ

1 + cot2 θ = cosec2 θ

Given in question 

sinθ – cosθ = 1/2

To Find out

sinθ + cosθ

The Solution

sinθ – cosθ = 1/2

On squaring both sides we get,

(sinθ – cosθ)² = (1/2)²

=sin²θ + cos²θ – 2 sinθcosθ = 1/4

Using the identity sin²θ + cos²θ = 1 we get

=1 – 2 sinθcosθ = 1/4

=2sinθcosθ = 1- (1/4) = 3/4

(sinθ +cosθ)² = sin²θ + cos²θ + 2 sinθcosθ

= 1 + 3/4 = 7/4

sinθ + cosθ = √(7/4) = (√7)/2