Grade 11 · Math · Algebra 2

11th grade Trig values by reference angle and quadrant sign, and the reciprocal ratios worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Trig values by reference angle and quadrant sign, and the reciprocal ratios

Grade 11 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

1.
Zee's bike wheel turns 510° from the positive x-axis. What is sin 510°?
- -1/2
- -√3/2
- √3/2
- 1/2
2.
Esme works out tan 330° on a unit circle worksheet. What is tan 330°?
- -√3
- √3/3
- -√3/3
- 1/2
3.
Jun turns a clock hand -210°, clockwise from the positive x-axis. What is cos(-210°)?
- √3/2
- -1/2
- 1/2
- -√3/2
Kira's robot drives around a unit circle on a floor grid and stops at (-5/13, 12/13) after a turn θ. What is sec θ?
Luz marks the point (15/17, -8/17) on a unit circle worksheet, at the end of a turn θ. What is csc θ?
Milo's robot drives around a unit circle on a floor grid and stops at (-60/61, 11/61) after a turn θ. What is cot θ?
Pia finds sin 200° on a calculator, to the nearest thousandth, for a unit circle worksheet. What is sin 200°?
Ren's robot turns 4 radians, and Ren finds cos 4 on a calculator to the nearest thousandth. What is cos 4?
Tala finds tan 160° on a calculator, to the nearest thousandth, for a unit circle worksheet. What is tan 160°?
Zee's robot turns 5 radians, and Zee finds sin 5 on a calculator to the nearest thousandth. What is sin 5?

11th grade Trig values by reference angle and quadrant sign, and the reciprocal ratios worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Trig values by reference angle and quadrant sign, and the reciprocal ratios. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell the signs of cos θ and sin θ from the quadrant.
I can find sin, cos and tan of any special angle from its reference angle and quadrant.
I can find csc, sec and cot as reciprocals, exactly or on a calculator in the right mode.

Standard: F-TF.A.2, F-TF.C.8 (related)

Words to know

reference angle: The acute angle between the end of the turn and the x-axis.

cosecant (csc): 1 ÷ sin θ.

secant (sec): 1 ÷ cos θ.

cotangent (cot): cos θ ÷ sin θ, the flip of tan θ.

reciprocal: 1 divided by a number: the fraction flipped, same sign.

degree mode / radian mode: The calculator setting that says which unit an angle is in.

Common mistakes

Used the right size of value but the Quadrant I sign. Ask which quadrant the angle ends in, and whether its point is left or right, up or down.

Swapped sine and cosine. Say together: the point is (cos, sin), across first, then up.

Measured the reference angle to the y-axis. Ask which axis the reference angle always uses (the x-axis).

Questions parents ask

What is the most common mistake with trig values by reference angle and quadrant sign, and the reciprocal ratios?

Used the right size of value but the Quadrant I sign. Ask which quadrant the angle ends in, and whether its point is left or right, up or down.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

See all Algebra 2

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records