Skip to content
MathSolver Pro
  • Open the math solver
  • Ask the AI tutor
  • Find an AP course
  • Create a quiz
  • Open the calculator
  • Graphing Calculator
  • Browse all calculators
  • Read math guides
↑ ↓Enter to open · Esc to close
Solve a problem
Unit circleTrigonometryHigh schoolabout 1:05

Find sin, cos and tan of π/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, 1); tan θ = undefined.

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 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    Find sin, cos and tan of π/2 on the unit circle.
  2. 2. Steps, part 1
    1. θ=90∘=π2 rad\theta = 90^\circ = \frac{\pi}{2}\ \text{rad}
      Convert radians to degrees (multiply by 180/π)
    2. Locate the terminal side: on the positive y-axis
    3. (cos⁡θ,sin⁡θ)=(0, 1)(\cos\theta, \sin\theta) = \left(0,\ 1\right)
      Read the exact coordinates from the reference angle and apply the quadrant signs
    4. tan⁡θ=sin⁡θcos⁡θ=undefined\tan\theta = \frac{\sin\theta}{\cos\theta} = \text{undefined}
      Tangent = sine ÷ cosine
  3. 3. Steps, part 2
    1. csc⁡θ=1,sec⁡θ=undefined,cot⁡θ=0\csc\theta = 1,\quad \sec\theta = \text{undefined},\quad \cot\theta = 0
      Reciprocal functions
  4. 4. The answer
    (cos⁡θ,sin⁡θ)=(0, 1)(\cos\theta, \sin\theta) = \left(0,\ 1\right)

    sin θ = 1, cos θ = 0, tan θ = undefined

  5. 5. Check
    • cos²θ + sin²θ = 1 (must equal 1).

Transcript

The problem. Here is the problem: Find sin, cos and tan of pi/2 on the unit circle. Unit circle values for 90° (pi/2 rad).

Steps, part 1. Convert radians to degrees (multiply by 180/pi). Locate the terminal side: on the positive y-axis. Quadrantal angles land on an axis, so one coordinate is 0. Read the exact coordinates from the reference angle and apply the quadrant signs. Tangent equals sine divided by cosine.

Steps, part 2. Reciprocal functions.

The answer. So the answer is (cos theta, sin theta) equals (0, 1); tan theta equals undefined. 90° (pi/2 rad) ends on the positive y-axis. sin theta equals 1, cos theta equals 0, tan theta equals undefined, csc theta equals 1, sec theta equals undefined, cot theta equals 0.

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.

More lessons like this

Find sin, cos and tan of π/2 on the unit circle (Lesson)