Problems on Trigonometric Ratios of an Angle

We will learn how to solve different types of problems on trigonometric ratios of an angle.

1. Which of the six trigonometric function are positive for x = -10π/3?

Solution: 

Given, x = -10π/3

We know that terminal position of x + 2nπ, where n ∈ Z, is the same as that of x.

Here, -10π/3 + 2 × 2π = 2π/3, which lies in the second quadrant.

Note: This process of finding a co-terminal angle or reference number results in an angle or number α, 0 ≤ α < 2π, so that we can determine in which quadrant the given angle or number lies.

Therefore, x = -10π/3 lies in the second quadrant.

Hence, sin x and csc x are positive while the other four trigonometric functions i.e. cos x, tan x, cot x and sec x are negative.

 

2. Express cos (- 1555°) in terms of the ratio of a positive angle less than 30°.

Solution:

cos(- 1555°) = cos 1555°, since we know cos (- θ) = cos θ]

= cos (17 × 90° + 25°)

= - sin 25°; since the angle 1555° lies in the second d quadrant and cos ratio is negative in this quadrant. Again, in  the angle 1555° = 17 × 90° + 25°, multiplier of 90° is 17, which is an odd integer ; for this reason cos ratio has changed to sin.

Note: The trigonometrical ratio of an angle of any magnitude can always be expressed in terms of ratio of a positive angle less than 30°.

 

3. If θ = 170° find the sign of (sin θ + cos θ)

Solution: 

sin θ = sin 170° = sin (2 × 90° - 10°) = sin 10°

and cos θ = cos 170° = cos (1 × 90° + 80°)= - sin 80°

Therefore, sin θ + cos θ = sin 10° - sin 80°

Since sin 10° > 0, sin 80° > 0 and sin 80° > sin 10°, thus sin 10° - sin 80° < 0 (i.e. negative) so, the value of (sin θ + cos θ) is negative.

4. Find the value of cos 200° sin 160° + sin (- 340°) cos (- 380°).

Solution:

Given, cos 200° sin 160° + sin (- 340°) cos (- 380°)

= cos (2 × 90° + 20°) sin (1 × 90° + 70°) + (- sin 340°) cos 380°

= - cos 20° cos 70° - sin (3 × 90° + 70°) cos (4 × 90° + 20°)

= - cos 20° cos 700 - (- cos 70°) cos 20°

= - cos 200 cos 70° + cos 70° cos 20°

= 0

 Trigonometric Functions




11 and 12 Grade Math

From Problems on Trigonometric Ratios of an Angle to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Adding 5-digit Numbers with Regrouping | 5-digit Addition |Addition

    Mar 18, 24 02:31 PM

    Adding 5-digit Numbers with Regrouping
    We will learn adding 5-digit numbers with regrouping. We have learnt the addition of 4-digit numbers with regrouping and now in the same way we will do addition of 5-digit numbers with regrouping. We…

    Read More

  2. Adding 4-digit Numbers with Regrouping | 4-digit Addition |Addition

    Mar 18, 24 12:19 PM

    Adding 4-digit Numbers with Regrouping
    We will learn adding 4-digit numbers with regrouping. Addition of 4-digit numbers can be done in the same way as we do addition of smaller numbers. We first arrange the numbers one below the other in…

    Read More

  3. Worksheet on Adding 4-digit Numbers without Regrouping | Answers |Math

    Mar 16, 24 05:02 PM

    Missing Digits in Addition
    In worksheet on adding 4-digit numbers without regrouping we will solve the addition of 4-digit numbers without regrouping or without carrying, 4-digit vertical addition, arrange in columns and add an…

    Read More

  4. Adding 4-digit Numbers without Regrouping | 4-digit Addition |Addition

    Mar 15, 24 04:52 PM

    Adding 4-digit Numbers without Regrouping
    We will learn adding 4-digit numbers without regrouping. We first arrange the numbers one below the other in place value columns and then add the digits under each column as shown in the following exa…

    Read More

  5. Addition of Three 3-Digit Numbers | With and With out Regrouping |Math

    Mar 15, 24 04:33 PM

    Addition of Three 3-Digit Numbers Without Regrouping
    Without regrouping: Adding three 3-digit numbers is same as adding two 3-digit numbers.

    Read More