In Problems 77-88, use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator. 77. sin 40° + cos? 40° 78. sec? 18° – tan 18° \ 79. sin 80° csc 80° 80. tan 10° cot 10° sin 40° cos 20° 81. tan 40° 82. cot 20° 83. cos 400° - sec 40° 84. tan 200° - cot 20° cos 40° sin 20° 85. sin(-) se 2 37 COs 18 sin (- 20°) 87. sin 70° csc 86. sec + tan 200° 88. + tan(-70°) 18 cos 380° cos (-430°)

A sinewave has a frequency of 685 Hz (cycles per second). What is the corresponding period of this sinewave expressed in msto 3 significant figures (see Study Note 7.1 in the Using Numbers (maths) booklet)? If the time period value you calculated above, is now reduced by a factor of 3, what will be the resulting frequency of the sinewave? Express your answer in kHz to 3 significant figures. Note: In the second part of this question, to avoid possible rounding errors in your calculations, use the actual sinewave period value from the first part, not the rounded value to 3 significant figures.

10. Find the exact value of the following functions without using a calculator. THERE SHOULD BE NO DECIMALS GIVEN AS ANSWERS! ONLY EXACT VALUES a. sin(-315°) b. cot (플) c. sec(135°)

sec"lx=cos"1 ! prove that X= cos