Grade 10 - Trigonometry

(Sample Printed worksheet)

Answer The Following

1)Simplify 3(sin4θ + cos4θ) - 2(sin6θ + cos6θ)
2)Simplify cos3θ sin3(90-θ) + sin3θ cos3(90-θ) + 3 cos2θ sin2θ
3)If α + β = 90, simplify .
4)Simplify
5)Simplify

Choose correct answer(s) from given choice

6)(cosθ - secθ)(cosecθ - sinθ) = ?
a. sinθ cosθ b.  
-1
sinθ cosθ
 
c.  
1
sinθ cosθ
 
d. - sinθ cosθ
7)A 2√3 m high pole casts 2 m long shadow on the ground. Find the angle of Sun's elevation.
a. 60 b. 30
c. 45 d. 37.5
8)A spherical balloon of radius 15 feet subtends an angle 60 at the eye of an observer. If the angle of elevation of its centre is 30, find the height of the centre of the balloon.
a. feet b. feet
c. feet d. feet
9)If cosec θ = a/b and 0 > θ > 90, find value of cot θ.
a. b.
c. d.
10)Simplify
a. cos2θ - sin2θ b. sinθ + cosθ
c. sin2θ - cos2θ d. sinθ - cosθ

Answers

1) 1
Step 1
= 3 (sin4θ + cos4θ) - 2 [ (sin2θ)3 + (cos2θ)3 } ]
Step 2
= 3 (sin4θ + cos4θ) - 2 [ (sin2θ + cos2θ) {(sin2θ)2 + (cos2θ)2 - sin2θ cos2θ } ]
Step 3
Since sin2θ + cos2θ = 1
=3 (sin4θ + cos4θ) - 2 {sin4θ + cos4θ - sin2θ cos2θ }
Step 4
= sin4θ + cos4θ + 2 sin2θ cos2θ
Step 5
= (sin2θ + cos2θ)2 = 12 = 1

2) 1
Step 1
Since sin(90-θ) = cos θ and cos(90-θ) = sin θ, expression can be rewritten as following
= (cos2θ)3 + (sin2θ)3 + 3 cos2θ sin2θ
Step 2
Since x3 + y3 = ( x + y ) ( x2 + y2 - xy)
= (cos2θ + sin2θ ) [ (cos2θ)2 + (sin2θ)2 - cos2θ sin2θ ] + 3 cos2θ sin2θ
Step 3
Since cos2θ + sin2θ =1 and x2 + y2 = (x+y)2 - 2 xy)
= (cos2θ + sin2θ ) [ (cos2θ + sin2θ)2 - 2 cos2θ sin2θ - cos2θ sin2θ] + 3 cos2θ sin2θ
= [ 1 - 3 cos2θ sin2θ ] + 3 cos2θ sin2θ
= 1

3) cos α
Step 1
It is given that α + β = 90, therefore
β = 90 - α
Step 2
Replace β with 90 - α in given expression
S =

⇒ S =
Step 3
Using trigonometrical identities
⇒ S =

⇒ S =

⇒ S = cos α

4) 0
Step 1
On adding two fractions
=
Step 2
=
Step 3
=
Step 4
=

5) 2 tanθ
Step 1
=
Step 2
=
Step 3
=

6) d. - sinθ cosθ
7) a. 60
Step 1
In following figure, AC shows the pole and AB is its shadow, and angle ∠B is the angle of Sun's elevation.
Step 2
tan(∠B) = AC/AB
⇒ tan(∠B) = (2√3)/(2)
⇒ tan(∠B) = √3
Step 3
We know that tan(60) = √3, therefore,
⇒ ∠B = 60

8) d. feet
9) d.
Step 1
We know that,
cot θ = √(cosec2θ - 1)
Step 2
Now replace value of cosec(θ) in above equation
⇒ cot(θ) =
Step 3
Simplify RHS of above equation

⇒ cot(θ) =

10) b. sinθ + cosθ
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