𝒔𝒊𝒏 𝟏𝟑𝟓 𝟎 = 𝒔𝒊𝒏 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 = 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒔𝒔𝒊𝒊𝒏𝒏 𝒔𝒊𝒏 𝟏𝟑𝟓 𝟎 = 𝒔𝒊𝒏 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 = 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐 𝟏𝟑𝟓 𝟎 𝟏𝟏𝟑𝟑𝟓𝟓 𝟏𝟑𝟓 𝟎 𝟎𝟎 𝟏𝟑𝟓 𝟎 = 𝒔𝒊𝒏 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 = 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒔𝒔𝒊𝒊𝒏𝒏 𝒔𝒊𝒏 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 = 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 𝟗𝟎 𝟎 𝟗𝟗𝟎𝟎 𝟗𝟎 𝟎 𝟎𝟎 𝟗𝟎 𝟎 +𝟒𝟒𝟓𝟓 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 𝟎𝟎 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 = 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐 𝐜𝐜𝐨𝐨𝐬𝐬 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐 𝟒𝟓 𝟎 𝟒𝟒𝟓𝟓 𝟒𝟓 𝟎 𝟎𝟎 𝟒𝟓 𝟎 = 𝟐 𝟐 𝟐 𝟐 𝟐𝟐 𝟐 𝟐 𝟐 𝟐𝟐 𝟐 𝟐 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒔𝒊𝒏 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 = 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒔𝒊𝒏 𝟏𝟑𝟓 𝟎 = 𝒔𝒊𝒏 𝟗𝟎 𝟎 +𝟒𝟓 𝟎 = 𝐜𝐨𝐬 𝟒𝟓 𝟎 = 𝟐 𝟐
𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 = 𝐜𝐨𝐬 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 = −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 𝐜𝐜𝐨𝐨𝐬𝐬 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 𝟏𝟓𝟎 𝟎 𝟏𝟏𝟓𝟓𝟎𝟎 𝟏𝟓𝟎 𝟎 𝟎𝟎 𝟏𝟓𝟎 𝟎 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 = 𝐜𝐨𝐬 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 = −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐 = 𝐜𝐨𝐬 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 = −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐 𝐜𝐜𝐨𝐨𝐬𝐬 𝐜𝐨𝐬 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 = −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 𝟏𝟖𝟎 𝟎 𝟏𝟏𝟖𝟖𝟎𝟎 𝟏𝟖𝟎 𝟎 𝟎𝟎 𝟏𝟖𝟎 𝟎 −𝟑𝟑𝟎𝟎 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 𝟎𝟎 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 = −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐 −𝐜𝐜𝐨𝐨𝐬𝐬 −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐 𝟑𝟎 𝟎 𝟑𝟑𝟎𝟎 𝟑𝟎 𝟎 𝟎𝟎 𝟑𝟎 𝟎 =− 𝟑 𝟐 𝟑 𝟑 𝟑𝟑 𝟑 𝟑 𝟐 𝟐𝟐 𝟑 𝟐 −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐 𝐜𝐨𝐬 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 = −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 = 𝐜𝐨𝐬 𝟏𝟖𝟎 𝟎 −𝟑𝟎 𝟎 = −𝐜𝐨𝐬 𝟑𝟎 𝟎 =− 𝟑 𝟐
𝒔𝒊𝒏 𝟏𝟑𝟓 𝟎 = 𝒔𝒊𝒏 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 = 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒔𝒔𝒊𝒊𝒏𝒏 𝒔𝒊𝒏 𝟏𝟑𝟓 𝟎 = 𝒔𝒊𝒏 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 = 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐 𝟏𝟑𝟓 𝟎 𝟏𝟏𝟑𝟑𝟓𝟓 𝟏𝟑𝟓 𝟎 𝟎𝟎 𝟏𝟑𝟓 𝟎 = 𝒔𝒊𝒏 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 = 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒔𝒔𝒊𝒊𝒏𝒏 𝒔𝒊𝒏 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 = 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 𝟏𝟖𝟎 𝟎 𝟏𝟏𝟖𝟖𝟎𝟎 𝟏𝟖𝟎 𝟎 𝟎𝟎 𝟏𝟖𝟎 𝟎 −𝟒𝟒𝟓𝟓 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 𝟎𝟎 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 = 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒄𝒄𝒐𝒐𝒔𝒔 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐 𝟒𝟓 𝟎 𝟒𝟒𝟓𝟓 𝟒𝟓 𝟎 𝟎𝟎 𝟒𝟓 𝟎 = 𝟐 𝟐 𝟐 𝟐 𝟐𝟐 𝟐 𝟐 𝟐 𝟐𝟐 𝟐 𝟐 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒔𝒊𝒏 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 = 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐 𝒔𝒊𝒏 𝟏𝟑𝟓 𝟎 = 𝒔𝒊𝒏 𝟏𝟖𝟎 𝟎 −𝟒𝟓 𝟎 = 𝒄𝒐𝒔 𝟒𝟓 𝟎 = 𝟐 𝟐
𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 = 𝐜𝐨𝐬 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 =− 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 𝐜𝐜𝐨𝐨𝐬𝐬 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 𝟏𝟓𝟎 𝟎 𝟏𝟏𝟓𝟓𝟎𝟎 𝟏𝟓𝟎 𝟎 𝟎𝟎 𝟏𝟓𝟎 𝟎 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 = 𝐜𝐨𝐬 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 =− 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐 = 𝐜𝐨𝐬 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 =− 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐 𝐜𝐜𝐨𝐨𝐬𝐬 𝐜𝐨𝐬 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 =− 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 𝟗𝟎 𝟎 𝟗𝟗𝟎𝟎 𝟗𝟎 𝟎 𝟎𝟎 𝟗𝟎 𝟎 +𝟔𝟔𝟎𝟎 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 𝟎𝟎 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 =− 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐 𝐬𝐬𝐢𝐢𝐧𝐧 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐 𝟔𝟎 𝟎 𝟔𝟔𝟎𝟎 𝟔𝟎 𝟎 𝟎𝟎 𝟔𝟎 𝟎 =− 𝟑 𝟐 𝟑 𝟑 𝟑𝟑 𝟑 𝟑 𝟐 𝟐𝟐 𝟑 𝟐 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐 𝐜𝐨𝐬 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 =− 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐 𝐜𝐨𝐬 𝟏𝟓𝟎 𝟎 = 𝐜𝐨𝐬 𝟗𝟎 𝟎 +𝟔𝟎 𝟎 =− 𝐬𝐢𝐧 𝟔𝟎 𝟎 =− 𝟑 𝟐
Есептеңіз:
𝐭𝐠 𝟏𝟐𝟎 𝟎 = 𝐭𝐠 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 = −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑 𝐭𝐠 𝟏𝟐𝟎 𝟎 𝐭𝐭𝐠𝐠 𝐭𝐠 𝟏𝟐𝟎 𝟎 𝟏𝟐𝟎 𝟎 𝟏𝟏𝟐𝟐𝟎𝟎 𝟏𝟐𝟎 𝟎 𝟎𝟎 𝟏𝟐𝟎 𝟎 𝐭𝐠 𝟏𝟐𝟎 𝟎 𝐭𝐠 𝟏𝟐𝟎 𝟎 = 𝐭𝐠 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 = −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑 = 𝐭𝐠 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 = −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑 𝐭𝐭𝐠𝐠 𝐭𝐠 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 = −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 𝟏𝟖𝟎 𝟎 𝟏𝟏𝟖𝟖𝟎𝟎 𝟏𝟖𝟎 𝟎 𝟎𝟎 𝟏𝟖𝟎 𝟎 −𝟔𝟔𝟎𝟎 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 𝟎𝟎 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 = −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑 −𝐭𝐭𝐠𝐠 −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑 𝟔𝟎 𝟎 𝟔𝟔𝟎𝟎 𝟔𝟎 𝟎 𝟎𝟎 𝟔𝟎 𝟎 =− 𝟑 𝟑 𝟑𝟑 𝟑 −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑 𝐭𝐠 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 = −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑 𝐭𝐠 𝟏𝟐𝟎 𝟎 = 𝐭𝐠 𝟏𝟖𝟎 𝟎 −𝟔𝟎 𝟎 = −𝐭𝐠 𝟔𝟎 𝟎 =− 𝟑
𝐭𝐠 𝟏𝟐𝟎 𝟎 = 𝐭𝐠 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 = −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑 𝐭𝐠 𝟏𝟐𝟎 𝟎 𝐭𝐭𝐠𝐠 𝐭𝐠 𝟏𝟐𝟎 𝟎 𝟏𝟐𝟎 𝟎 𝟏𝟏𝟐𝟐𝟎𝟎 𝟏𝟐𝟎 𝟎 𝟎𝟎 𝟏𝟐𝟎 𝟎 𝐭𝐠 𝟏𝟐𝟎 𝟎 𝐭𝐠 𝟏𝟐𝟎 𝟎 = 𝐭𝐠 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 = −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑 = 𝐭𝐠 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 = −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑 𝐭𝐭𝐠𝐠 𝐭𝐠 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 = −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 𝟗𝟎 𝟎 𝟗𝟗𝟎𝟎 𝟗𝟎 𝟎 𝟎𝟎 𝟗𝟎 𝟎 +𝟑𝟑𝟎𝟎 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 𝟎𝟎 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 = −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑 −𝐜𝐜𝐭𝐭𝐠𝐠 −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑 𝟑𝟎 𝟎 𝟑𝟑𝟎𝟎 𝟑𝟎 𝟎 𝟎𝟎 𝟑𝟎 𝟎 =− 𝟑 𝟑 𝟑𝟑 𝟑 −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑 𝐭𝐠 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 = −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑 𝐭𝐠 𝟏𝟐𝟎 𝟎 = 𝐭𝐠 𝟗𝟎 𝟎 +𝟑𝟎 𝟎 = −𝐜𝐭𝐠 𝟑𝟎 𝟎 =− 𝟑
𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝟐 (𝟏+ 𝟑 ) 𝟒 𝐬𝐬𝐢𝐢𝐧𝐧 𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝟐 (𝟏+ 𝟑 ) 𝟒 𝟕𝟓 𝟎 𝟕𝟕𝟓𝟓 𝟕𝟓 𝟎 𝟎𝟎 𝟕𝟓 𝟎 = 𝟐 (𝟏+ 𝟑 ) 𝟒 𝟐 𝟐 𝟐𝟐 𝟐 (𝟏𝟏+ 𝟑 𝟑 𝟑𝟑 𝟑 ) 𝟐 (𝟏+ 𝟑 ) 𝟒 𝟒𝟒 𝟐 (𝟏+ 𝟑 ) 𝟒 𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝟐 (𝟏+ 𝟑 ) 𝟒
𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝐬𝐬𝐢𝐢𝐧𝐧 𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟕𝟓 𝟎 𝟕𝟕𝟓𝟓 𝟕𝟓 𝟎 𝟎𝟎 𝟕𝟓 𝟎 = 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝐬𝐬𝐢𝐢𝐧𝐧 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟑𝟎 𝟎 𝟑𝟑𝟎𝟎 𝟑𝟎 𝟎 𝟎𝟎 𝟑𝟎 𝟎 +𝟒𝟒𝟓𝟓 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟎𝟎 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎
𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝐬𝐬𝐢𝐢𝐧𝐧 𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟕𝟓 𝟎 𝟕𝟕𝟓𝟓 𝟕𝟓 𝟎 𝟎𝟎 𝟕𝟓 𝟎 = 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝐬𝐬𝐢𝐢𝐧𝐧 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟑𝟎 𝟎 𝟑𝟑𝟎𝟎 𝟑𝟎 𝟎 𝟎𝟎 𝟑𝟎 𝟎 +𝟒𝟒𝟓𝟓 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟎𝟎 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎 𝐬𝐢𝐧 𝟕𝟓 𝟎 = 𝐬𝐢𝐧 𝟑𝟎 𝟎 +𝟒𝟓 𝟎
Сабақ мақсаты:
• Тригонометриялық қосу формулаларын қорытып шығару;
• тригонометриялық өрнектерді ықшамдауда қосу формулаларын қолдану.
Бағалау критериі:
Оқушылар:
• Қосу формулаларын қорытып шығарады;
• Тригонометриялық өрнектерді ықшамдауда қосу формулаларын қолданады.
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С вами с 2009 года.