Find the general solution for:-

~Please show your work

~Thank you!

Step-by-step explanation:

we would like to solve the following trigonometric equation:

the left hand side can be rewritten using angle sum indentity of sin which is given by:

therefore Let

Thus substitute:

simplify addition:

keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:

take inverse trig and that yields:

add π to both sides of the second equation and that yields:

sin function has a period of 2nπ thus add the period:

divide I equation by 4 and II by -4 which yields:

recall that,-½(nπ)=½(nπ) therefore,

by using a calculator we acquire:

hence,

the general solution for: for the trig equation are

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places