Trig Rules

Question 1

∫sec(x)tan(x)

Answer 1

sec(x) + C

Question 2

∫csc(x) cot(x)

Answer 2

-csc(x) +C

Question 3

∫csc²(x)

Answer 3

-cot(x) + C

Question 4

∫tan(x)

Answer 4

ln| sec(x)| +C

Question 5

∫sec(x)

Answer 5

ln |sec(x) + tan(x)| +C

Question 6

∫1/(a² +x²)

Answer 6

1/a tan−1(x/a) +C

Question 7

∫ 1/ √(a- x²)

Answer 7

sin−1( x/a) +C

Question 8

∫ ln(x)

Answer 8

xln(x) -x +C

Question 9

(sec(x))’

Answer 9

sec(x)tan(x)

Question 10

(csc(x))’

Answer 10

-csc(x) cot(x)

Question 11

(cot(x))’

Answer 11

-csc² (x)

Question 12

∫a^x

Answer 12

1/ln(a)*a^x

Question 13

(cos-1(x))’

Answer 13

-1/√(1-x²)

Question 14

(tan-1(x))’

Answer 14

1/(1+x²)

Question 15

lim x–>0 (sin(x)/x)

Answer 15

1

Question 16

lim x–>0 (cos(x) -1)/x

Answer 16

0

Question 17

lim x–> 0 sin(ax)/x

Answer 17

a

Question 18

lim x–>0 sin(ax)/ sin(bx)

Answer 18

a/b

Question 19

Trig Identity: sin(2x)

Answer 19

=2sin(x)cos(x)

Question 20

Trig Identity: cos(2x)

Answer 20

cos²(x) -sin²(x)= 1-2sin²(x)

Question 21

Trig Identity: cos²(x)

Answer 21

(1/2)(1 + cos(2x))

Question 22

Trig Identity: sin²(x)

Answer 22

(1/2)(1 - cos(2x))

Question 23

Trig Identity: sec²(x)

Answer 23

1+ tan²(x)

Question 24

Trig Identity: csc²(x)

Answer 24

cot²(x) +1

Question 25

∫sin²(x)

Answer 25

(x/2)- (1/2)sin(x)cos(x)

Question 26

∫cos²(x)

Answer 26

(x/2)+ (1/2)sin(x)cos(x)

Question 27

Trig Substitution √ ̅ (a²- x²)

Answer 27

x= asin(θ)
dx= acos (θ)
√ ̅ (a²- x²) = acos(θ)

Question 28

Trig Substitution √ ̅(x²+ a²)

Answer 28

x= a tan(θ)
dx= asec²(θ)
√ ̅(x²+ a²)= a sec(θ)

Question 29

Trig Substitution √ ̅(x²- a²)

Answer 29

x= asec(θ)
dx= asec(θ)tan(θ)
√ ̅(x²- a²)= a tan(θ)