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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

Here, $cotx space equals space 3 over 4$

sinx<0, cosx<0, tanx>0, cosecx<0, secx<0, cotx>0 (∵ x lies in quadrant III)

Now,    $cosec squared straight x space equals space 1 plus cot squared straight x space space rightwards double arrow space space space space cosec squared straight x space equals space 1 plus 9 over 16 space equals space 25 over 16 space space space rightwards double arrow space space space space cosecx space equals space plus-or-minus 5 over 4$

$rightwards double arrow$    $cosecx space equals space minus 5 over 4$ (∵ cosecx < 0)

$sinx space equals space 1 over cosecx space equals space fraction numerator 1 over denominator negative 5 divided by 4 end fraction space equals space minus 4 over 5$

$space space space cotx space equals space cosx over sinx$

$rightwards double arrow$    $space space space space space space space 3 over 4 equals space fraction numerator cosx over denominator left parenthesis negative 4 divided by 5 right parenthesis end fraction space space space or space cosx space equals space minus 3 over 5$

   $space space space space space space secx space equals space 1 over cosx space equals space fraction numerator 1 over denominator negative 3 divided by 5 end fraction space equals space minus 5 over 3$

   $tanx space equals space 1 over cotx space equals space fraction numerator 1 over denominator 3 divided by 4 end fraction space equals space 4 over 3$