Question

Use the addition of sines identity to evaluate sin255 degrees

what would theta 1 and theta 2 be?

Answer 1

keep in mind that
90 +45 = 135
60+60 = 120

and those are common known angles
thus keep in mind that 135 + 120 = 255

Answer 2

so would I need to solve for 2 different equations?

Answer 3

one being sin(90+45) and the other sin(60+60) ?

Answer 4

@jdoe0001

Answer 5

well... nope
notice the instruction "Use the addition of sines identity"

thus \(\bf sin({\color{brown}{ \alpha}} + {\color{blue}{ \beta}})=sin({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}}) + cos({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}})
\\ \quad \\
thus
\\ \quad \\
sin(255^o)\\ \quad \\ sin({\color{brown}{ 135^o}} + {\color{blue}{ 120^o}})=sin({\color{brown}{ 135^o}})cos({\color{blue}{ 120^o}}) + cos({\color{brown}{ 135^o}})sin({\color{blue}{ 120^o}})\)

Answer 6

and you can get those from your Unit Circle

Answer 7

Is the answer -1/2? @jdoe0001