Math+C30

=[Math C30|]=

Use this space to discuss what we did today including any assignments. Also, summarize your learning here. Use text, examples, any diagrams or pictures to help you with your explanation. If we have used the smart board, you can place the file here if you wish or even use a video.

1.1 sin- y/r csc- r/y cos- x/r sec-r/x tan-y/x cot- x/y Exact values:
 * || 0 || 30 || 45 || 60 || 90 ||
 * sin || 0 || 1/2 || root2/2 || root3/2 || 1 ||
 * cos || 1 || root3/2 || root2/2 || 1/2 || 0 ||
 * tan || 0 || root3/3 || 1 || root3 || undefined ||

reference angles- always positive use to find exact trig ratio

The 45 – 45 – 90 Theorem In a 45 – 45- 90 triangle the legs are of equal length and the hypotenuse is root 2 times as long as either leg.

The 30 - 60 - 90 Theorem In a 30 - 60 - 90 triangle the hypotenuse is 2 times as long as the shorter leg. The longer leg is root 3 times as long as the shorter leg.


 * Chapter 3

1** solving right triangles: SOH CAH TOA angle of elevation: look up from horizontal angle of depression: look down from horizontal 3.2 Law of cosines c2=a2 + b2 - 2abcosC 3.3 Law of Sines a/sinA= b/sinB 3.4 ambiguous case Summary if in ABC we are given an acute angle (B) a side adjacent to B (say c) and a side opposite B (b) then: 1) no triangle if b is less than csinB 2) one triangle if b =csinB 3) two triangles if csinB is less than b less than c 4) one triangle if b is greater than equal to c \obtuse 1) no triangle if b is less than or equal to c 2) ONE TRIANGLE IF b IS GREATER THAN c 3.5 Solving General triangles -Draw careful sketch
 * no rounded numbers till the end
 * longest side is always opposite the largest angle. shortest side is always opposite the shortest angle
 * if it is a triangle the side opposite the given angle must be at least as long as the length of the side adjacent to the given angle multiplied by the sine of the given angle.

3.6 Areas of a triangle Case 1: base and altitude are given just use 1/2 bh Case 2: S.A.S K=1/2absinC Case 3: A.S.A K=a2sinBsinC/2sinA Case 4: S.S.S K=Root s(s-a)(s-b)(s-c) s=a+b+c/2