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Chapter 8: Q. 27 (page 516)

Find the exact value of the expression-
$\cos 35 ° \sin 55 ° + \sin 35 ° \cos 55 °$

Short Answer

Expert verified

The required value is,

$\cos 35 ° \sin 55 ° + \sin 35 ° \cos 55 ° =$ $1$

Step by step solution

01

Step 1. Given information

Given expression,

$\cos 35 ° \sin 55 ° + \sin 35 ° \cos 55 °$

02

Step 2. Calculation

Solving the given expression,

$\cos 35 ° \sin 55 ° + \sin 35 ° \cos 55 ° = \cos (90 ° - 55 °) \sin 55 ° + \sin (90 ° - 55 °) \cos 55 ° = \sin 55 ° \sin 55 ° + \cos 55 ° \cos 55 °$ ---------- $\sin (90 ° - θ) = \cos θ, \cos (90 ° - θ) = \sin θ$

$= \sin^{2} 55 ° + \cos^{2} 55 ° = 1$ ----------------We know, $\sin^{2} θ + \cos^{2} θ = 1$

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Most popular questions from this chapter

The displacement d (in meters) of an object at time t (in seconds) is given $d = 2 \cos (2 t)$

(a) Describe the motion of the object.

(b) What is the maximum displacement from its resting position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

What do you do first if you are asked to solve a triangle and are given one side and two angles?

The Original Ferris Wheel George Washington Gale Ferris, Jr., designed the original Ferris wheel for the 1893 World’s Columbian Exposition in Chicago, Illinois. The wheel had 36 equally spaced cars each the size of a school bus. The distance between adjacent cars was approximately 22 feet. Determine the diameter of the wheel to the nearest

foot.

Find an exact value of each expression, without using a calculator $\frac{s e c 55}{c s c 35}$

For any triangle, derive the formula $a = b \cos C + c \cos B$

$[H i n t : U s e t h e f a c t t h a t \sin A = \sin (180^{\circ} - B - C)]$

See all solutions

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