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Test: Trigonometric Ratios - SAT MCQ


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10 Questions MCQ Test Mathematics for SAT - Test: Trigonometric Ratios

Test: Trigonometric Ratios for SAT 2024 is part of Mathematics for SAT preparation. The Test: Trigonometric Ratios questions and answers have been prepared according to the SAT exam syllabus.The Test: Trigonometric Ratios MCQs are made for SAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Trigonometric Ratios below.
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Test: Trigonometric Ratios - Question 1

What is the value of cos A sec A + sin A cosec A – tan A cot A?

Detailed Solution for Test: Trigonometric Ratios - Question 1

Cos A sec A = 1
Similarly sin A cosec A = 1 and tan A cot A = 1
∴ cos A sec A + sin A cosec A – tan A cot A = 1 + 1 – 1 = 1

Test: Trigonometric Ratios - Question 2

If tan θ = 3/4 then the value of sinθ is _________

Detailed Solution for Test: Trigonometric Ratios - Question 2



Hence, BC = 3k, AC = 4k
Using Pythagoras theorem
AB2 = AC2 + BC2
AB2 = 4k2 + 3k2
AB = 5k

Test: Trigonometric Ratios - Question 3

If tan α = √3 and cosec β = 1, then the value of α – β?

Detailed Solution for Test: Trigonometric Ratios - Question 3

tan α = √3 and tan 60° = √3
∴ α = 60°
Cosec β = 1 and cosec 90° = 1
∴ β = 90°
α – β = 60 – 90 = -30°

Test: Trigonometric Ratios - Question 4

If sin A = 8/17, what will be the value of cos A sec A?

Detailed Solution for Test: Trigonometric Ratios - Question 4

sin A = 8/17
cos A sec A can be written as
∴ cos A sec A = 1

Test: Trigonometric Ratios - Question 5

If sin (A + B) = √3/2 and tan (A – B) = 1. What are the values of A and B?

Detailed Solution for Test: Trigonometric Ratios - Question 5

The value of sin (A + B) = √3/2 and sin 60° = √3/2
∴ A + B = 60     (1)
The value of tan (A – B) = 1 and tan 45° = 1
∴ A – B = 45     (2)
Adding equation (1) and (2)
A + B = 60
+ A – B = 45
– – – – – – – – – – – – –
2 A = 105
A = 52.5
∴ B = 7.5

Test: Trigonometric Ratios - Question 6

In a right angled triangle, the trigonometric function that is equal to the ratio of the side opposite a given angle to the hypotenuse is called cosine.

Detailed Solution for Test: Trigonometric Ratios - Question 6


In this ∆ ABC,

Test: Trigonometric Ratios - Question 7

What is the value of sin30°cos15° + cos30°sin15°?

Detailed Solution for Test: Trigonometric Ratios - Question 7

 

sin30°cos15° + cos30°sin15° = sin⁡45° = 1/√2

Test: Trigonometric Ratios - Question 8

In triangle ABC, right angled at C, then the value of cosec (A + B) is __________

Detailed Solution for Test: Trigonometric Ratios - Question 8

Since the triangle is right angles at C,
The sum of the remaining two angles will be 90
∴ cosec(A + B) = Cosec 90° = 1

Test: Trigonometric Ratios - Question 9

The value of each of the trigonometric ratios of an angle depends on the size of the triangle and does not depend on the angle.

Detailed Solution for Test: Trigonometric Ratios - Question 9


Consider, two triangles ABC and DEF
In ∆ABC,

From these examples it is evident that the value of the trigonometric ratios depends on their angle and not on their lengths.    

Test: Trigonometric Ratios - Question 10

If cos θ = 3/4 then value of cos 2θ is ___________

Detailed Solution for Test: Trigonometric Ratios - Question 10

 

cos 2θ = 2cos θ2 – 1
cos θ = 3/4
cos 2θ = 2(3/4)2 – 1
= 1/8

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