In the circle diagram below, a right triangle can be inscribed in the circle in the following manner. ![]() Throughout this unit, it will be helpful for you to learn the exact values of sin, cos, and tan of these angles. The ratios of the lengths of the sides of each triangle is shown below. These angles are 30°, 45°, 60°, and any angle having any of these three as reference angles. There are certain angles whose exact trig functions can be found without a calculator. These three ratios are the most common trig ratios. The trig (short for trigonometry) ratios sine(sin), cosine (cos) and tangent (tan) are based on properties of right triangles. The unit circle with critical values labeled in radian and degrees angles is shown below: In addition all whole number multiples will also be critical values for all angles ≤ 360°. If you remember that 180° = π radians, it is easy to remember the other angles. The critical values in Quadrant I are as follows: These angle measures are equivalent to radian measures of and, respectively. The word trigonometry comes from the Greek words for “triangle measure Angles whose measures are multiples of 30° and 45° are commonly used in trigonometry. Trigonometry is the study of angles and triangles. S top!Go to Questions #10-17 about this section, then return to continue on to the next section. You can convert from degrees to radians and visa versa.Įxample #1: Convert 40° from degrees to radians and radians to degrees. Thus, an angle of 180° = π radians and 90° =. Therefore an angle representing one complete revolution of the circle measures 2π radians or 360°. So the circumference of a unit circle is 2π(1) or 2π radians. The circumference of any circle is 2π r, where r is the radius of the circle. ![]() ![]() The radian measure of an angle is equal to the length of the arc on the unit circle (a circle centered at the origin with a radius of 1) that is intercepted by the angle in standard position. Another unit of angle measure is called the radian, which is better suited for certain mathematical development, scientific work and engineering applications. S top!Go to Questions #6-9 about this section, then return to continue on to the next section.ĭegree measure of angles is used extensively in engineering, surveying and navigation.
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