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Trigonometric Functions

Short Answer Type

21. The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of radians in the greatest angle is 60 :

straight pi

. Find the angles in degrees.

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22. Assuming the average distance of the earth from the sun to be 149,700,000 km, and the angle subtended by the sun at the eye of a person on the earth to be 32’, find the sun’s diameter.

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23. Find the angle between the minute hand of a clock and the hour hand when the time is 7:20 A.M.

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24. Find the values of other five trigonometric functions of the following:

cosx space equals space minus 1 half comma space straight x

lies in third quadrant

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25. Find the values of other five trigonometric functions of the following:

sinx space equals space 3 over 5 comma space straight x

lies in second quadrant

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26. Find the values of other five trigonometric functions of the following:

cotx space equals space 3 over 4 comma space space straight x

lies in third quadrant

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27. Find the values of the trigonometric functions in the following:

sin space 765 degree

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28. Find the values of the trigonometric functions in the following:

$cosec left parenthesis negative 1410 degree right parenthesis$

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∴ We may add or subtract an integral multiple of $2 straight pi space or space 360 degree$ to convert the angle to an acute angle. Also, tanx and cotx are periodic functions of period $straight pi space left parenthesis 180 degree right parenthesis.$

Therefore, we may add or subtract an integral multiple of $straight pi$ to convert the angle to an acute angle.

$cosec left parenthesis negative 1410 degree right parenthesis space equals space cosec left square bracket left parenthesis negative 1410 degree plus 4 left parenthesis 360 degree right parenthesis right square bracket$ [∵ Period is $2 straight pi space equals space 360 degree$ ]

$space space space space equals space cosec space left parenthesis negative 1410 degree plus 1440 degree right parenthesis space equals space cosec 30 degree space equals space fraction numerator 1 over denominator sin 30 degree end fraction space equals space fraction numerator 1 over denominator 1 divided by 2 end fraction space equals space 2$

Hence, $cosec left parenthesis negative 1410 degree right parenthesis space equals space 2$