Simplifying Expressions and Trigonometric Functions

The video tutorial covers mathematical operations involving square roots, cosine, and tangent. It explains how to manipulate square roots in equations, calculate cosine using trigonometric identities, and find tangent values while rationalizing denominators. The tutorial also demonstrates how to calculate the cosine of 105 degrees using the unit circle and trigonometric identities.

What is the result of pulling a constant out from under a square root?

• The constant remains unchanged.

• The constant is halved.

• The constant is squared.

• The square root of the constant is taken.

When simplifying expressions, why might you change a '1' to '2/2'?

• To eliminate the denominator.

• To make the expression more complex.

• To facilitate division by 2.

• To change the value of the expression.

What is the cosine of pi/8 expressed in terms of square roots?

• Square root of 1 minus square root of 2.

• Square root of 2 minus square root of 3.

• Square root of 2 plus square root of 3.

• Square root of 1 plus square root of 2.

How can you express cosine of pi/4 in a simplified form?

• Square root of 2 over 2.

• 1 over square root of 2.

• Square root of 3 over 2.

• Square root of 2 over 3.

What is the relationship between tangent and sine/cosine?

• Tangent is cosine divided by sine.

• Tangent is the sum of sine and cosine.

• Tangent is sine divided by cosine.

• Tangent is the product of sine and cosine.

How do you rationalize a denominator involving square roots?

• Multiply by the square root.

• Subtract the square root from the numerator.

• Add the square root to the numerator.

• Multiply by the conjugate of the denominator.

What is the simplified form of tangent pi/8?

• Square root of 2 plus 1.

• Square root of 2 minus 1.

• 1 minus square root of 2.

• 1 plus square root of 2.

How can you find the cosine of 105° using known angles?

• By using the sine of 105°.

• By using the cosine of 210°.

• By using the tangent of 210°.

• By using the sine of 210°.

What is the cosine of 210°?

• Square root of 3 over 2.

• Negative square root of 3 over 2.

• Square root of 2 over 2.

• Negative square root of 2 over 2.

What is the result of simplifying 1 - square root of 3 over 2?

• 1 minus square root of 3 over 4.

• 2 minus square root of 3 over 4.

• 1 plus square root of 3 over 4.

• Square root of 3 over 4.