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°)

Q: √3 Find x when sinx = -1 2 between [0,360]

A: Given, sin(x)=-32                 x∈[0°,360°]

Q: Find the largest value of x that satisfies: loge (2) – log,(r + 1) = 6

A: Use the properties of logarithmic function, to rewrite the given equation.…

Q: 9. In what situation would you use the sine or cosine laws rather than just simple trigonometric…

A:

Q: 6. The point A (6, -2) is on the terminal side of an angle in standard position. Determine the exact…

A: The figure

Q: (a) 1² + 4.x + 3

A: Here we have to evaluate the integration by using trigonometric substitution method.

Q: What is the photon frequency (Terahertz = 1012 Hz) needed to move an electron in 1 to a higher…

A: We will find out the required value.

Q: 7. Use Trigonometric Substitution to evaluate -1

A: Here we have to integrate by the trigonometric substitution.  I=∫x3x2-1dx

Q: 4. Using your a.)calculator and b.) Excel , find the roots of x, with percentage error at less than…

A: Note: Here, we want the percentage error less than or equal to 5%. So, here we will find the root up…

Q: Find x, if artan x/2 = pi/4

A: arc tan (x/2 )= pi/4 and as we know tan(pi/4) = 1

Q: 4. Use Regiomontanus' sine table to find the remaining angles in the right triangle if you know that…

A: Answers are following in explanation step.Explanation:

Q: 3. (7x – 1)- 125°

A:

Q: Tan ( 3θ - 4 degrees ) = 1/ cot ( 5θ - 8 degrees)

A: Solve:

Q: Identify the amplitude, frequency, period, and interval of one cycle for each of the following. y =…

A: Let suppose f(x)=asin(bx+c)+dwhere a = amplitudeb = frequency period = 2πfrequencyInterval of one…

Q: In Problems 35–46, convert each angle in degrees to radians. Express your answer as a multiple of T.…

A:

Q: 4. 2 -2 -4- -6+ -8-

A: The objective is to find period and amplitude of the given function.

Q: Question 22, problem is in photo

A: Standard normal distribution:The standard normal distribution is a special case of normal…

Q: La Grande Roue de Montréal is the largest Ferris wheel in Canada and the fourth largest in the…

A:

Q: Example 2.22. Use the method of false position, to find the fourth root of 32 correct to three…

A:

Q: 8. Use Trigonometric Substitution to evaluate x'V4+x?

A: We will use standard formulae of trigonometry.

Q: A sinewave has a frequency of 685 Hz (cycles per second). What is the corresponding period of this…

A: Given: A sinewave has a frequency of 685 Hz (cycles per second ).

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.