Write as a trigonometric ratio of an acute angle
Sin 95
Sin 95 can be written as the trigonometric ratio of an acute angle as follows:
Sin 95 = Sin (180 - 95) = Sin 85
The sine function is defined as the ratio of the length of the side opposite the acute angle to the length of the hypotenuse in a right triangle. Since we are given the angle of 95 degrees, we need to find the sine of an acute angle.
To find the sine of an acute angle, we need to use its reference angle, which is the acute angle formed between the terminal side of the given angle and the x-axis. The reference angle for 95 degrees is 180 degrees - 95 degrees = 85 degrees.
Therefore, the sine of 95 degrees can be written as the sine of its reference angle:
sin 95 = sin 85
To write sin 95 as a trigonometric ratio of an acute angle, we can use a trigonometric identity known as the cofunction identity. According to this identity, the sine of an angle is equal to the cosine of its complementary angle.
Since 90 degrees is the complement of 0 degrees, we can rewrite 95 degrees as the sum of 90 degrees and 5 degrees:
95 degrees = 90 degrees + 5 degrees
Now, using the cofunction identity, we can write:
sin 95 = cos 5
Therefore, sin 95 can be expressed as the trigonometric ratio cos 5 of an acute angle.