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Algebra and Trigonometry Exam 1 Review – Step-by-Step Guidance

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Q1. Convert the angle 36° from degrees to radians. Express the answer as a multiple of .

Background

Topic: Angle Conversion (Degrees to Radians)

This question tests your ability to convert an angle measured in degrees to radians, which is a fundamental skill in trigonometry.

Key formula:

To convert degrees to radians, use:

Step-by-Step Guidance

  1. Write down the given angle in degrees: .

  2. Set up the conversion using the formula: .

  3. Simplify the fraction to its lowest terms.

  4. Express your answer as a multiple of .

Try solving on your own before revealing the answer!

Final Answer:

We simplified to , so radians.

Q2. Convert the angle -270° from degrees to radians. Express the answer as a multiple of .

Background

Topic: Angle Conversion (Degrees to Radians)

This question checks your understanding of converting negative angles from degrees to radians.

Key formula:

Step-by-Step Guidance

  1. Write the given angle: .

  2. Apply the conversion formula: .

  3. Simplify the fraction .

  4. Express your answer as a multiple of .

Try solving on your own before revealing the answer!

Final Answer:

Dividing by $180-\frac{3}{2}-270^\circ = -\frac{3\pi}{2}$ radians.

Q3. Convert the angle 43° from degrees to radians. Express your answer as a decimal rounded to two decimal places.

Background

Topic: Angle Conversion (Degrees to Radians, Decimal Form)

This question asks you to convert degrees to radians and round the answer to two decimal places.

Key formula:

Step-by-Step Guidance

  1. Write the given angle: .

  2. Set up the conversion: .

  3. Calculate the value of using .

  4. Round your answer to two decimal places.

Try solving on your own before revealing the answer!

Final Answer: 0.75 radians

After calculation and rounding, radians.

Q4. Convert the angle 58° from degrees to radians. Express your answer as a decimal rounded to two decimal places.

Background

Topic: Angle Conversion (Degrees to Radians, Decimal Form)

This question is similar to the previous one, focusing on decimal conversion.

Key formula:

Step-by-Step Guidance

  1. Write the given angle: .

  2. Set up the conversion: .

  3. Calculate using .

  4. Round your answer to two decimal places.

Try solving on your own before revealing the answer!

Final Answer: 1.01 radians

After calculation and rounding, radians.

Q5. Convert the angle radians to degrees.

Background

Topic: Angle Conversion (Radians to Degrees)

This question tests your ability to convert an angle from radians to degrees.

Key formula:

Step-by-Step Guidance

  1. Write the given angle: radians.

  2. Set up the conversion: .

  3. Notice that cancels out in the numerator and denominator.

  4. Multiply by $180$ to get the degree measure.

Try solving on your own before revealing the answer!

Final Answer: -75°

Multiplying gives .

Q6. Convert the angle radians to degrees.

Background

Topic: Angle Conversion (Radians to Degrees)

This question is similar to the previous one, focusing on positive radian values.

Key formula:

Step-by-Step Guidance

  1. Write the given angle: radians.

  2. Set up the conversion: .

  3. Cancel in the numerator and denominator.

  4. Multiply by $180$ to get the degree measure.

Try solving on your own before revealing the answer!

Final Answer: 105°

Multiplying gives .

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