Use the given function values and trigonometric identities (including the relationship between a trigonometric function and its cofunction of a complementary angle) to find the indicated trigonometric functions.
sec Q = 5
tan = 2sqrt6
a) cos Q
b) cotQ
c) cot(90 degrees - Q)
d) sin Q
To find the trigonometric functions using the given function values and trigonometric identities, we can make use of the definitions of the trigonometric functions and the relationships between them.
a) To find cos Q, we can use the definition cos Q = 1 / sec Q. Since sec Q = 5, we can substitute it into the definition to get cos Q = 1 / 5.
b) To find cot Q, we can use the definition cot Q = 1 / tan Q. Since tan Q = 2√6, we can substitute it into the definition to get cot Q = 1 / (2√6).
c) To find cot(90 degrees - Q), we can use the relationship between the cotangent and the tangent of a complementary angle, which states that cot(90 degrees - Q) = tan Q. Since tan Q = 2√6, cot(90 degrees - Q) = 2√6.
d) To find sin Q, we can use the relationship between sine and cosine, which states that sin Q = √(1 - cos^2 Q). We already found cos Q to be 1 / 5. Substituting it into the formula, we get sin Q = √(1 - (1/5)^2) = √(1 - 1/25) = √(24/25) = √24 / 5.
Therefore, the values of the indicated trigonometric functions are:
a) cos Q = 1 / 5
b) cot Q = 1 / (2√6)
c) cot(90 degrees - Q) = 2√6
d) sin Q = √24 / 5