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Trigonometry: Sine, Cosine, Tangent

Learn the basic trigonometry ratios and how to use them to find missing sides or angles in right-angled triangles. Let's get started! 🚀

Trigonometry: Sine, Cosine, Tangent - introduction visual

Video Lesson

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Flashcards

Review key concepts visually

Definitions, ratios, and visuals of sine, cosine, and tangent shown in a right triangle.A right triangle with 30° angle, opposite side 4 cm. Using the ratio of sin 30°, solve the hypotenuse, which is 8 cm.The application of using tangent to find the missing side of a right triangle with a 50-degree angle and a known side of 5 cm.Finding the angle using cosine in a right triangle with sides 4 cm and 8 cm, showing the calculation cos theta = 1/2 and theta = cos⁻¹(1/2) = 60°.Common values of sine, cosine, and tangent for 30°, 60°, and 45° with right triangles and ratios.

🛎️ What Are sin, cos, and tan?

  • These are ratios used in right-angled triangles
  • Once the angle is given, the ratios are fixed

🛎️ Using sin, cos, and tan

  • SOH: sin⁡θ=oppositehypotenuse\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}
  • CAH: cos⁡θ=adjacenthypotenuse\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}
  • TOA: tan⁡θ=oppositeadjacent\tan\theta = \frac{\text{opposite}}{\text{adjacent}}

🛎️ Finding a Missing Side

  • Choose sin, cos, or tan based on the sides you know and the side you want
  • Substitute the values and rearrange to find the unknown side

🛎️ Finding a Missing Angle

  • Write the correct trig ratio first (sin, cos, or tan)
  • Use the inverse function on the calculator (sin⁡−1\sin^{-1}, cos⁡−1\cos^{-1}, or tan⁡−1\tan^{-1})

🛎️ Common Trigonometric Values

  • You should know the exact values for 30°, 45°, and 60° without a calculator
  • Having these triangles in your head helps you see the ratios instantly

Practice Questions

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Interactive Activity

Explore trigonometric ratios in a right triangle

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