Question

6 (a) Solve, for-180° << 180°, the equation

5 sin 20 = 9 tan 0
10 sine = 9 tand.
-
giving your answers, where necessary, to one decimal place.
[Solutions based entirely on graphical or numerical methods are not acceptable.]
(b) Deduce the smallest positive solution to the equation
5 sin (2x - 50°) = 9 tan (x - 25°)
(6)
(2)

Answer 1

To solve trigonometric equations involving sine and tangent, we can use trigonometric identities to rewrite the equations in terms of sine. Then, we can solve for the variable using algebraic methods.

Step-by-step explanation:

To solve the equation 5 sin 20 = 9 tan 0, we need to use trigonometric identities to rewrite sin 20 and tan 0 in terms of sine.

Using the trigonometric identity sin(2x) = 2sin(x)cos(x), we can rewrite 5sin(20) as 5(2sin(20)cos(20)).

Next, using the trigonometric identity tan(x) = sin(x)/cos(x), we can rewrite 9tan(0) as 9sin(0)/cos(0). By substituting these expressions into the equation, we can solve for cos(20) and find the value of x.

For part (b), we can use the same trigonometric identities and algebraic methods to solve for x in the equation 5sin(2x - 50) = 9tan(x - 25).

Learn more about Trigonometric equations involving sine and tangent