Podcast
Questions and Answers
Which trigonometric functions are abbreviated as sin, cos, and tan?
Which trigonometric functions are abbreviated as sin, cos, and tan?
- Arcsine, Arccosine, and Arctangent
- Hyperbolic Sine, Hyperbolic Cosine, and Hyperbolic Tangent
- Secant, Cosecant, and Cotangent
- Sine, Cosine, and Tangent (correct)
What is the ratio of the opposite side to the hypotenuse in a right-angled triangle?
What is the ratio of the opposite side to the hypotenuse in a right-angled triangle?
- Sine (correct)
- Cosecant
- Tangent
- Cosine
Which angle is often labeled as θ in trigonometry?
Which angle is often labeled as θ in trigonometry?
- The obtuse angle
- The acute angle
- The angle of interest (correct)
- The right angle
What is the ratio of the adjacent side to the hypotenuse in a right-angled triangle?
What is the ratio of the adjacent side to the hypotenuse in a right-angled triangle?
Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle?
Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle?
Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle?
Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle?
In a right-angled triangle, if the length of the hypotenuse is 10 units and the length of the opposite side is 8 units, what is the value of the sine of the angle between the hypotenuse and the opposite side?
In a right-angled triangle, if the length of the hypotenuse is 10 units and the length of the opposite side is 8 units, what is the value of the sine of the angle between the hypotenuse and the opposite side?
If the length of the adjacent side in a right-angled triangle is 5 units and the length of the hypotenuse is 13 units, what is the value of the cosine of the angle between the adjacent side and the hypotenuse?
If the length of the adjacent side in a right-angled triangle is 5 units and the length of the hypotenuse is 13 units, what is the value of the cosine of the angle between the adjacent side and the hypotenuse?
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Study Notes
Trigonometric Functions
- The abbreviations sin, cos, and tan represent the sine, cosine, and tangent functions, respectively.
- The sine function is defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle.
- The cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right-angled triangle.
- The tangent function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.
Applying Trigonometric Functions
- If the length of the hypotenuse is 10 units and the length of the opposite side is 8 units, the value of the sine of the angle between the hypotenuse and the opposite side is 8/10 or 0.8.
- If the length of the adjacent side is 5 units and the length of the hypotenuse is 13 units, the value of the cosine of the angle between the adjacent side and the hypotenuse is 5/13 or approximately 0.38.
Notation and Labeling
- The angle is often labeled as θ (theta) in trigonometry.
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