Solve a problem

Unit circleTrigonometryHigh schoolabout 2:13

Find sin, cos and tan of 1.2 on the unit circle: animated lesson

A narrated, step-by-step unit circle video lesson with captions. Final answer: (cos θ, sin θ) ≈ (0.3623577545, 0.932039086); tan θ ≈ 2.572151622.

SpeedLanguage

Chapters

Transcript

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.9 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Find sin, cos and tan of 1.2 on the unit circle.
2. Steps, part 1
1. $\theta = 68.75493542^\circ = 1.2\ \text{rad}$
  Convert radians to degrees (multiply by 180/π)
2. $68.75493542^\circ$
  Find the coterminal angle between 0° and 360°
3. Locate the terminal side: in Quadrant I
4. $\theta_{\text{ref}} = 68.75493542^\circ$
  Reference angle (acute angle to the x-axis)
3. Steps, part 2
1. $(\cos\theta, \sin\theta) = \left(0.3623577545,\ 0.932039086\right)$
  Evaluate the coordinates (this angle is not a multiple of 15°, so values are decimal approximations)
2. $\tan\theta = \frac{\sin\theta}{\cos\theta} = \approx 2.572151622$
  Tangent = sine ÷ cosine
3. $\csc\theta = \approx 1.072916378,\quad \sec\theta = \approx 2.759703601,\quad \cot\theta = \approx 0.3887795694$
  Reciprocal functions
4. The answer
$(\cos\theta, \sin\theta) = \left(0.3623577545,\ 0.932039086\right)$
sin θ ≈ 0.932039086, cos θ ≈ 0.3623577545, tan θ ≈ 2.572151622
5. Check
- cos²θ + sin²θ = 1 (must equal 1).

Transcript

The problem. Here is the problem: Find sin, cos and tan of 1.2 on the unit circle. Unit circle values for 68.75493542° (1.2 rad).

Steps, part 1. Convert radians to degrees (multiply by 180/pi). Find the coterminal angle between 0° and 360°. Add or subtract full turns of 360° (2pi); trigonometric values repeat every full turn. Locate the terminal side: in Quadrant I. In Quadrant I sine and cosine are both positive (“All Students Take Calculus”). Reference angle (acute angle to the x-axis).

Steps, part 2. Evaluate the coordinates (this angle is not a multiple of 15°, so values are decimal approximations). Tangent equals sine divided by cosine. Reciprocal functions.

The answer. So the answer is (cos theta, sin theta) approximately (0.3623577545, 0.932039086); tan theta approximately 2.572151622. 68.75493542° (1.2 rad) ends in Quadrant I with a reference angle of 68.75493542°. sin theta approximately 0.932039086, cos theta approximately 0.3623577545, tan theta approximately 2.572151622, csc theta approximately 1.072916378, sec theta approximately 2.759703601, cot theta approximately 0.3887795694.

Check. cos squaredtheta plus sin squaredtheta equals 1 (must equal 1).

About unit circle

Read sine, cosine and tangent of standard angles from the unit circle.

Find sin, cos and tan of 1.2 on the unit circle (Lesson)