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Trigonometry: Sine, Cosine, Tangent

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Trigonometry: Sine, Cosine, Tangent

Geometry and Measures Trigonometry: Sine, Cosine, Tangent

Courses Overview

🎬 Video Tutorial

(0:01) Basic Trigonometry: Sine, cosine, and tangent depend only on the angle $\theta$ in a right-angled triangle; they do not change with the size of the triangle.
(0:22) Trigonometric Ratios (sin cos tan): $\sin \theta = \large \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos \theta = \large \frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan \theta = \large \frac{\text{opposite}}{\text{adjacent}}$.
(0:56) Using Trigonometry to Find Lengths: Learn with examples how to apply trigonometry formulas to calculate missing sides of a right-angled triangle.
(2:14) Finding Angles: Find the unknown angle $\theta$ using inverse functions like $\cos^{-1}$ on a calculator.
(3:04) Trigonometry Table: Memorise trigonometric values for common angles (30°, 45°, 60°) to simplify calculations.

📂 Revision Cards

Definitions, ratios, and visuals of sine, cosine, and tangent shown in a right triangle. — 1) What is sin, cos, and tan?

A right triangle with 30° angle, opposite side 4 cm. Using the ratio of sin 30°, solve the hypotenuse, which is 8 cm. — 2) Trigonometry: Sine for Finding Side

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. — 3) Trigonometry: Tangent for Finding Side

Finding the angle using cosine in a right triangle with sides 4 cm and 8 cm, showing the calculation cos ? = 1/2 and ? = cos?¹(1/2) = 60°. — 4) Trigonometry: Cosine for Finding Angle

Common values of sine, cosine, and tangent for 30°, 60°, and 45° with right triangles and ratios. — 5) Trigonometry Table

🍪 Quiz Time - Practice Now!

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Trigonometry: Sine, Cosine, Tangent

1 / 6

Q: In a right-angled triangle, the opposite side is 3 cm, and the hypotenuse is 5 cm. What is the sine of the angle? $Right-angled triangle with sides labelled 3 cm and 5 cm, angle ? opposite the shorter side to be calculated.$

$\frac{5}{4}$

$\frac{4}{5}$

$\frac{3}{5}$

1

Feedback: Not quite! The sine formula is $sin(?) = \frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is 3 cm and the hypotenuse is 5 cm. So, the sine of the angle is $ \frac{3}{5}$.

Feedback: Well done! The sine formula is $sin(?) = \frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is 3 cm and the hypotenuse is 5 cm. So, the sine of the angle is $ \frac{3}{5}$.

2 / 6

Q: In a right-angled triangle, the adjacent side is 8 cm, and the hypotenuse is 10 cm. What is the cosine of the angle?

$Right-angled triangle with sides labelled 4 cm, 5 cm, and angle ? between them to be calculated.$

1

$\frac{5}{8}$

$\frac{4}{5}$

$\frac{7}{25}$

Feedback: Not quite! The cosine formula is $cos(?) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$. Here, the adjacent side is 8 cm and the hypotenuse is 10 cm. So, the cosine of the angle is $ \frac{8}{10} = \frac{4}{5}$.

Feedback: Well done! The cosine formula is $cos(?) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$. Here, the adjacent side is 8 cm and the hypotenuse is 10 cm. So, the cosine of the angle is $ \frac{8}{10} = \frac{4}{5}$.

3 / 6

Q: What is the sine of the angle?

$Right-angled triangle with sides labelled 8 cm and 16 cm, angle ? opposite the shorter side.$

1

$\frac{5}{16}$

$\frac{5}{8}$

$\frac{1}{2}$

Feedback: Not quite! The sine formula is $sin(?) = \frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is 8 cm and the hypotenuse is 16 cm, so the sine of the angle is $ \frac{8}{16} = \frac{1}{2}$.

Feedback: Well done! The sine formula is $sin(?) = \frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is 8 cm and the hypotenuse is 16 cm, so the sine of the angle is $ \frac{8}{16} = \frac{1}{2}$.

4 / 6

Q: What is the tangent of the angle?

$Right-angled triangle with sides labelled 5 cm, 12 cm and 13 cm, angle ? opposite the shorter.$

$\frac{5}{13}$

$\frac{12}{5}$

$\frac{12}{13}$

$\frac{5}{12}$

Feedback: Not quite! Using the tangent formula $tan(?) = \frac{\text{Opposite}}{\text{Adjacent}}$, here the opposite side is 5 cm and the adjacent side is 12 cm. So, the tangent of the angle is $ \frac{5}{12}$.

Feedback: Well done! Using the tangent formula $tan(?) = \frac{\text{Opposite}}{\text{Adjacent}}$, here the opposite side is 5 cm and the adjacent side is 12 cm. So, the tangent of the angle is $ \frac{5}{12}$.

5 / 6

Q: What is the cosine of the angle?

$Right-angled triangle with sides labelled 5 cm, 12 cm and 13 cm, angle ? opposite the shorter.$

$\frac{12}{13}$

$\frac{12}{5}$

$\frac{5}{13}$

$\frac{5}{12}$

Feedback: Not quite! Using the cosine formula $tan(?) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, here the adjacent side is 12 cm and the hypotenuse side is 13 cm. So, the tangent of the angle is $ \frac{12}{13}$.

Feedback: Well done! Using the cosine formula $tan(?) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, here the adjacent side is 12 cm and the hypotenuse side is 13 cm. So, the tangent of the angle is $ \frac{12}{13}$.

6 / 6

Q: Find the angle $\theta$ in the right-angled triangle.

$Right-angled triangle with sides labelled 8 cm and 16 cm, angle ? opposite the shorter side.$

$\frac{8}{16}$

$\frac{12}{13}$

$\frac{5}{12}$

$\frac{5}{13}$

Feedback: Not quite! The sine formula is $sin(?) = \frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is 8 cm and the hypotenuse is 16 cm, so $sin(?) = \frac{8}{16} = \frac{1}{2}$. To find $\theta$, we use the inverse sine function. On a calculator, enter $sin^{-1}(\frac{1}{2})$, and it will give the result $\theta = 30^\circ$.

Feedback: Well done! The sine formula is $sin(?) = \frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is 8 cm and the hypotenuse is 16 cm, so $sin(?) = \frac{8}{16} = \frac{1}{2}$. To find $\theta$, we use the inverse sine function. On a calculator, enter $sin^{-1}(\frac{1}{2})$, and it will give the result $\theta = 30^\circ$.

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