Trigonometric Identities and Functions

This video tutorial covers trigonometric identities, including reciprocal, quotient, and Pythagorean identities. It explains how to use these identities to determine function values and solve trigonometric problems. The video also includes examples and problem-solving techniques, emphasizing the application of identities in various scenarios. The tutorial concludes with a summary of key points.

Which of the following is a reciprocal identity?

• Cosine theta = adjacent / hypotenuse

• Sine theta = opposite / hypotenuse

• Secant theta = 1 / cosine theta

• Tangent theta = sine theta / cosine theta

Tags

CCSS.HSF.TF.C.8

What is the Pythagorean identity involving sine and cosine?

• Tangent squared theta + 1 = secant squared theta

• Sine squared theta + cosine squared theta = 1

• Sine theta = cosine theta

• 1 + cotangent squared theta = cosecant squared theta

How do you verify the identity sine squared theta + cosine squared theta = 1 using a right triangle?

• By using the definition of secant

• By applying the Pythagorean theorem

• By applying the law of sines

• By using the definition of tangent

Tags

CCSS.HSF.TF.C.8

If cosine theta = 3/4 and theta is in the 4th quadrant, what is sine theta?

• Square root of 7 over 4

• 3/4

• Negative square root of 7 over 4

• Negative 3/4

Tags

CCSS.HSF.TF.C.8

Given tangent theta = -5/3 in the 2nd quadrant, what is secant theta?

• 5/3

• Square root of 34 over 3

• Negative 5/3

• Negative square root of 34 over 3

Tags

CCSS.HSF.TF.C.8

How do you find sine theta if you know cosecant theta?

• Multiply by the reciprocal of tangent

• Take the reciprocal of cosecant theta

• Subtract 1 from cosecant theta

• Add 1 to cosecant theta

Tags

CCSS.HSF.TF.C.8

Which identity is used to find secant theta from tangent theta?

• Sine theta = 1 / cosecant theta

• 1 + cotangent squared theta = cosecant squared theta

• Tangent squared theta + 1 = secant squared theta

• Sine squared theta + cosine squared theta = 1

Tags

CCSS.HSF.TF.A.2

What is the value of r if the point (-2, -4) is on the terminal side of theta?

• Square root of 20

• 5

• 2 square root of 5

• 4

Tags

CCSS.HSF.TF.A.2

What is the cosine of theta if the point (-2, -4) is on the terminal side?

• Negative 2

• Square root of 5 over 5

• 2

• Negative square root of 5 over 5

Tags

CCSS.HSF.TF.C.8

If tangent theta = 2, what is cotangent theta?

• Negative 1/2

• 1/2

• Negative 2

• 2

Tags

CCSS.HSF.TF.C.8