Trig Special Angles

What is the sine of 30 degrees?

• 0.5

• 0.75

• 1.0

• 0.25

Answer explanation

The sine of 30 degrees is 0.5. This is a common trigonometric value that represents the ratio of the length of the side opposite an acute angle to the hypotenuse in a right triangle.

What is the cosine of 45 degrees?

• 0.577

• 0.866

• 0.7071

• 1.414

Answer explanation

The cosine of 45 degrees is 0.7071, which is the correct answer choice provided.

What is the tangent of 60 degrees?

• 0

• 1

• √3

• 2

Answer explanation

The tangent of 60 degrees is √3. In a 30-60-90 triangle, the tangent of 60 degrees is equal to the square root of 3.

What is the cotangent of 45 degrees?

• 2

• 1

• 0.5

• 3

Answer explanation

The cotangent of 45 degrees is equal to 1. Cotangent is the reciprocal of tangent, and the tangent of 45 degrees is 1, so the cotangent is also 1.

What is the secant of 30 degrees?

• 1/2

• 1/√3

• √3/2

• 2/√3

Answer explanation

The secant of an angle is the reciprocal of the cosine. Since the cosine of 30 degrees is √3/2, the secant of 30 degrees is 1/(√3/2) = 2/√3.

What is the cosecant of 60 degrees?

• 1

• 2√3/3

• 1/2

• 3/2

Answer explanation

The cosecant of 60 degrees is equal to 2√3/3. Cosecant is the reciprocal of the sine function, so csc(60°) = 1/sin(60°) = 1/(√3/2) = 2√3/3.

Calculate sin(30°) + cos(45°)

• 1.207

• 0.866

• 0.707

• 1.575

Answer explanation

sin(30°) = 0.5, cos(45°) = √2/2. Therefore, sin(30°) + cos(45°) = 0.5 + √2/2 = 1.207

Calculate tan(60°) - cot(45°)

• √3 + 1

• √3 - √2

• 1 - √3

• √3 - 1

Answer explanation

To calculate tan(60°) - cot(45°), we use the trigonometric identities tan(60°) = √3 and cot(45°) = 1. Therefore, tan(60°) - cot(45°) = √3 - 1.

Calculate sec(30°) / csc(60°)

• 2

• 0.5

• -1

• 1

Answer explanation

sec(30°) = 2, csc(60°) = 2, therefore sec(30°) / csc(60°) = 2 / 2 = 1. The correct answer is 1.

If sin(x) = 1/2, what is the value of x in degrees?

• 45

• 90

• 60

• 30

Answer explanation

The value of x in degrees when sin(x) = 1/2 is 30 degrees. This is because sin(30 degrees) = 1/2, making 30 the correct choice.